LMFDB - Embedded newform 729.2.g.a.28.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [729,2,Mod(28,729)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(729, base_ring=CyclotomicField(54))

chi = DirichletCharacter(H, H._module([44]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("729.28");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 729 = 3^{6} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	729.g (of order $27$, degree $18$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.82109430735$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$8$ over $\Q(\zeta_{27})$
Twist minimal:	no (minimal twist has level 81)
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			28.3
Character	$\chi$	$=$	729.28
Dual form			729.2.g.a.703.3

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.890910 + 0.585961i) q^{2} +(-0.341789 + 0.792356i) q^{4} +(-0.585850 + 0.620965i) q^{5} +(0.284505 + 0.0332539i) q^{7} +(-0.530120 - 3.00646i) q^{8} +O(q^{10})$	\(q+(-0.890910 + 0.585961i) q^{2} +(-0.341789 + 0.792356i) q^{4} +(-0.585850 + 0.620965i) q^{5} +(0.284505 + 0.0332539i) q^{7} +(-0.530120 - 3.00646i) q^{8} +(0.158079 - 0.896509i) q^{10} +(0.519011 - 1.73362i) q^{11} +(-0.325075 + 5.58132i) q^{13} +(-0.272954 + 0.137083i) q^{14} +(1.04960 + 1.11251i) q^{16} +(-4.42908 + 1.61205i) q^{17} +(-1.75427 - 0.638503i) q^{19} +(-0.291788 - 0.676441i) q^{20} +(0.553440 + 1.84862i) q^{22} +(-1.34612 + 0.157339i) q^{23} +(0.248347 + 4.26396i) q^{25} +(-2.98082 - 5.16294i) q^{26} +(-0.123590 + 0.214064i) q^{28} +(-5.35083 - 2.68729i) q^{29} +(-2.54206 - 3.41458i) q^{31} +(4.35412 + 1.03194i) q^{32} +(3.00131 - 4.03146i) q^{34} +(-0.187327 + 0.157186i) q^{35} +(-5.46107 - 4.58238i) q^{37} +(1.93704 - 0.459086i) q^{38} +(2.17748 + 1.43215i) q^{40} +(-9.58849 - 6.30645i) q^{41} +(12.3767 - 2.93332i) q^{43} +(1.19625 + 1.00377i) q^{44} +(1.10708 - 0.928949i) q^{46} +(1.22397 - 1.64408i) q^{47} +(-6.73148 - 1.59539i) q^{49} +(-2.71977 - 3.65328i) q^{50} +(-4.31129 - 2.16521i) q^{52} +(1.54131 - 2.66962i) q^{53} +(0.772454 + 1.33793i) q^{55} +(-0.0508455 - 0.872983i) q^{56} +(6.34175 - 0.741244i) q^{58} +(-0.361763 - 1.20837i) q^{59} +(1.09744 + 2.54416i) q^{61} +(4.26556 + 1.55254i) q^{62} +(-7.35831 + 2.67821i) q^{64} +(-3.27536 - 3.47168i) q^{65} +(-5.61273 + 2.81882i) q^{67} +(0.236491 - 4.06039i) q^{68} +(0.0747867 - 0.249805i) q^{70} +(-2.24048 + 12.7064i) q^{71} +(-1.11508 - 6.32396i) q^{73} +(7.55042 + 0.882517i) q^{74} +(1.10551 - 1.17178i) q^{76} +(0.205311 - 0.475965i) q^{77} +(-5.95312 + 3.91543i) q^{79} -1.30574 q^{80} +12.2378 q^{82} +(-11.3260 + 7.44925i) q^{83} +(1.59375 - 3.69472i) q^{85} +(-9.30768 + 9.86557i) q^{86} +(-5.48720 - 0.641362i) q^{88} +(0.0750415 + 0.425581i) q^{89} +(-0.278086 + 1.57711i) q^{91} +(0.335421 - 1.12038i) q^{92} +(-0.127083 + 2.18193i) q^{94} +(1.42423 - 0.715275i) q^{95} +(-6.92494 - 7.34001i) q^{97} +(6.93197 - 2.52303i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10}) $ 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8	$ 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} - 45 q^{20} + 9 q^{22} + 45 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28} - 36 q^{29} + 9 q^{31} + 99 q^{32} + 9 q^{34} - 9 q^{35} - 18 q^{37} - 18 q^{38} + 9 q^{40} - 27 q^{41} + 9 q^{43} - 54 q^{44} - 18 q^{46} + 99 q^{47} + 9 q^{49} - 126 q^{50} - 27 q^{52} - 45 q^{53} - 9 q^{55} + 225 q^{56} + 9 q^{58} - 72 q^{59} + 9 q^{61} - 81 q^{62} - 18 q^{64} + 81 q^{65} - 45 q^{67} - 117 q^{68} - 99 q^{70} + 90 q^{71} - 18 q^{73} - 81 q^{74} - 153 q^{76} - 81 q^{77} - 99 q^{79} + 288 q^{80} - 36 q^{82} - 45 q^{83} - 99 q^{85} - 81 q^{86} - 153 q^{88} + 81 q^{89} - 18 q^{91} - 207 q^{92} - 99 q^{94} + 171 q^{95} - 45 q^{97} - 81 q^{98}+O(q^{100}) $ 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8 - 18 * q^10 - 9 * q^11 + 9 * q^13 - 9 * q^14 + 9 * q^16 + 18 * q^17 - 18 * q^19 - 45 * q^20 + 9 * q^22 + 45 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 - 36 * q^29 + 9 * q^31 + 99 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 - 18 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 + 99 * q^47 + 9 * q^49 - 126 * q^50 - 27 * q^52 - 45 * q^53 - 9 * q^55 + 225 * q^56 + 9 * q^58 - 72 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 + 81 * q^65 - 45 * q^67 - 117 * q^68 - 99 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 - 153 * q^76 - 81 * q^77 - 99 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 - 99 * q^85 - 81 * q^86 - 153 * q^88 + 81 * q^89 - 18 * q^91 - 207 * q^92 - 99 * q^94 + 171 * q^95 - 45 * q^97 - 81 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/729\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{22}{27}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.890910	+	0.585961i	−0.629968	+	0.414337i	−0.823945	−	0.566669i	$-0.808232\pi$
$2$	−0.890910	+	0.585961i	−0.629968	+	0.414337i	0.193977	+	0.981006i	$0.437861\pi$
$3$		0			0
$3$		0			0
$4$	−0.341789	+	0.792356i	−0.170894	+	0.396178i
$5$	−0.585850	+	0.620965i	−0.262000	+	0.277704i	−0.844998	−	0.534770i	$-0.820398\pi$
$5$	−0.585850	+	0.620965i	−0.262000	+	0.277704i	0.582998	+	0.812474i	$0.301880\pi$
$6$		0			0
$7$	0.284505	+	0.0332539i	0.107533	+	0.0125688i	0.169689	−	0.985498i	$-0.445724\pi$
$7$	0.284505	+	0.0332539i	0.107533	+	0.0125688i	−0.0621562	+	0.998066i	$0.519798\pi$
$8$	−0.530120	−	3.00646i	−0.187426	−	1.06295i
$9$		0			0
$10$	0.158079	−	0.896509i	0.0499889	−	0.283501i
$11$	0.519011	−	1.73362i	0.156488	−	0.522706i	−0.843406	−	0.537277i	$-0.819453\pi$
$11$	0.519011	−	1.73362i	0.156488	−	0.522706i	0.999894	+	0.0145710i	$0.00463825\pi$
$12$		0			0
$13$	−0.325075	+	5.58132i	−0.0901596	+	1.54798i	0.585443	+	0.810714i	$0.300921\pi$
$13$	−0.325075	+	5.58132i	−0.0901596	+	1.54798i	−0.675602	+	0.737266i	$0.736116\pi$
$14$	−0.272954	+	0.137083i	−0.0729501	+	0.0366369i
$15$		0			0
$16$	1.04960	+	1.11251i	0.262400	+	0.278128i
$17$	−4.42908	+	1.61205i	−1.07421	+	0.390980i	−0.817749	−	0.575574i	$-0.804778\pi$
$17$	−4.42908	+	1.61205i	−1.07421	+	0.390980i	−0.256460	+	0.966555i	$0.582556\pi$
$18$		0			0
$19$	−1.75427	−	0.638503i	−0.402458	−	0.146483i	0.132857	−	0.991135i	$-0.457585\pi$
$19$	−1.75427	−	0.638503i	−0.402458	−	0.146483i	−0.535315	+	0.844652i	$0.679807\pi$
$20$	−0.291788	−	0.676441i	−0.0652458	−	0.151257i
$21$		0			0
$22$	0.553440	+	1.84862i	0.117994	+	0.394127i
$23$	−1.34612	+	0.157339i	−0.280686	+	0.0328074i	−0.255271	−	0.966870i	$-0.582165\pi$
$23$	−1.34612	+	0.157339i	−0.280686	+	0.0328074i	−0.0254146	+	0.999677i	$0.508091\pi$
$24$		0			0
$25$	0.248347	+	4.26396i	0.0496694	+	0.852791i
$26$	−2.98082	−	5.16294i	−0.584587	−	1.01254i
$27$		0			0
$28$	−0.123590	+	0.214064i	−0.0233563	+	0.0404542i
$29$	−5.35083	−	2.68729i	−0.993624	−	0.499017i	−0.123762	−	0.992312i	$-0.539496\pi$
$29$	−5.35083	−	2.68729i	−0.993624	−	0.499017i	−0.869862	+	0.493295i	$0.835792\pi$
$30$		0			0
$31$	−2.54206	−	3.41458i	−0.456568	−	0.613277i	0.512914	−	0.858440i	$-0.328566\pi$
$31$	−2.54206	−	3.41458i	−0.456568	−	0.613277i	−0.969482	+	0.245163i	$0.921159\pi$
$32$	4.35412	+	1.03194i	0.769706	+	0.182424i
$33$		0			0
$34$	3.00131	−	4.03146i	0.514721	−	0.691390i
$35$	−0.187327	+	0.157186i	−0.0316641	+	0.0265693i
$36$		0			0
$37$	−5.46107	−	4.58238i	−0.897794	−	0.753339i	0.0719637	−	0.997407i	$-0.477073\pi$
$37$	−5.46107	−	4.58238i	−0.897794	−	0.753339i	−0.969758	+	0.244068i	$0.921518\pi$
$38$	1.93704	−	0.459086i	0.314229	−	0.0744736i
$39$		0			0
$40$	2.17748	+	1.43215i	0.344290	+	0.226443i
$41$	−9.58849	−	6.30645i	−1.49747	−	0.984902i	−0.992563	−	0.121728i	$-0.961156\pi$
$41$	−9.58849	−	6.30645i	−1.49747	−	0.984902i	−0.504907	−	0.863174i	$-0.668473\pi$
$42$		0			0
$43$	12.3767	−	2.93332i	1.88742	−	0.447328i	0.887514	−	0.460780i	$-0.152430\pi$
$43$	12.3767	−	2.93332i	1.88742	−	0.447328i	0.999910	+	0.0134525i	$0.00428219\pi$
$44$	1.19625	+	1.00377i	0.180342	+	0.151325i
$45$		0			0
$46$	1.10708	−	0.928949i	0.163230	−	0.136966i
$47$	1.22397	−	1.64408i	0.178535	−	0.239814i	−0.703843	−	0.710356i	$-0.748534\pi$
$47$	1.22397	−	1.64408i	0.178535	−	0.239814i	0.882378	+	0.470542i	$0.155941\pi$
$48$		0			0
$49$	−6.73148	−	1.59539i	−0.961640	−	0.227913i
$50$	−2.71977	−	3.65328i	−0.384633	−	0.516652i
$51$		0			0
$52$	−4.31129	−	2.16521i	−0.597868	−	0.300261i
$53$	1.54131	−	2.66962i	0.211715	−	0.366701i	−0.740537	−	0.672016i	$-0.765429\pi$
$53$	1.54131	−	2.66962i	0.211715	−	0.366701i	0.952251	+	0.305315i	$0.0987619\pi$
$54$		0			0
$55$	0.772454	+	1.33793i	0.104158	+	0.180406i
$56$	−0.0508455	−	0.872983i	−0.00679452	−	0.116657i
$57$		0			0
$58$	6.34175	−	0.741244i	0.832713	−	0.0973301i
$59$	−0.361763	−	1.20837i	−0.0470975	−	0.157317i	0.931206	−	0.364493i	$-0.118758\pi$
$59$	−0.361763	−	1.20837i	−0.0470975	−	0.157317i	−0.978304	+	0.207177i	$0.933573\pi$
$60$		0			0
$61$	1.09744	+	2.54416i	0.140513	+	0.325747i	0.973912	−	0.226926i	$-0.0728674\pi$
$61$	1.09744	+	2.54416i	0.140513	+	0.325747i	−0.833399	+	0.552672i	$0.813608\pi$
$62$	4.26556	+	1.55254i	0.541726	+	0.197172i
$63$		0			0
$64$	−7.35831	+	2.67821i	−0.919789	+	0.334776i
$65$	−3.27536	−	3.47168i	−0.406258	−	0.430609i
$66$		0			0
$67$	−5.61273	+	2.81882i	−0.685705	+	0.344374i	−0.757307	−	0.653060i	$-0.773485\pi$
$67$	−5.61273	+	2.81882i	−0.685705	+	0.344374i	0.0716021	+	0.997433i	$0.477189\pi$
$68$	0.236491	−	4.06039i	0.0286787	−	0.492395i
$69$		0			0
$70$	0.0747867	−	0.249805i	0.00893872	−	0.0298574i
$71$	−2.24048	+	12.7064i	−0.265896	+	1.50797i	0.500576	+	0.865693i	$0.333122\pi$
$71$	−2.24048	+	12.7064i	−0.265896	+	1.50797i	−0.766472	+	0.642278i	$0.777989\pi$
$72$		0			0
$73$	−1.11508	−	6.32396i	−0.130511	−	0.740164i	−0.977881	−	0.209161i	$-0.932927\pi$
$73$	−1.11508	−	6.32396i	−0.130511	−	0.740164i	0.847370	−	0.531002i	$-0.178184\pi$
$74$	7.55042	+	0.882517i	0.877718	+	0.102591i
$75$		0			0
$76$	1.10551	−	1.17178i	0.126811	−	0.134412i
$77$	0.205311	−	0.475965i	0.0233974	−	0.0542412i
$78$		0			0
$79$	−5.95312	+	3.91543i	−0.669778	+	0.440520i	−0.838323	−	0.545174i	$-0.816464\pi$
$79$	−5.95312	+	3.91543i	−0.669778	+	0.440520i	0.168545	+	0.985694i	$0.446093\pi$
$80$	−1.30574			−0.145986
$81$		0			0
$82$	12.2378			1.35144
$83$	−11.3260	+	7.44925i	−1.24319	+	0.817661i	−0.988772	−	0.149433i	$-0.952255\pi$
$83$	−11.3260	+	7.44925i	−1.24319	+	0.817661i	−0.254421	+	0.967094i	$0.581885\pi$
$84$		0			0
$85$	1.59375	−	3.69472i	0.172866	−	0.400749i
$86$	−9.30768	+	9.86557i	−1.00367	+	1.06383i
$87$		0			0
$88$	−5.48720	−	0.641362i	−0.584937	−	0.0683694i
$89$	0.0750415	+	0.425581i	0.00795438	+	0.0451115i	0.988527	−	0.151047i	$-0.0482644\pi$
$89$	0.0750415	+	0.425581i	0.00795438	+	0.0451115i	−0.980572	+	0.196158i	$0.937153\pi$
$90$		0			0
$91$	−0.278086	+	1.57711i	−0.0291514	+	0.165326i
$92$	0.335421	−	1.12038i	0.0349700	−	0.116808i
$93$		0			0
$94$	−0.127083	+	2.18193i	−0.0131076	+	0.225049i
$95$	1.42423	−	0.715275i	0.146123	−	0.0733857i
$96$		0			0
$97$	−6.92494	−	7.34001i	−0.703121	−	0.745265i	0.273114	−	0.961982i	$-0.411947\pi$
$97$	−6.92494	−	7.34001i	−0.703121	−	0.745265i	−0.976234	+	0.216717i	$0.930465\pi$
$98$	6.93197	−	2.52303i	0.700235	−	0.254865i
$99$		0			0
$100$	−3.46345	−	1.26059i	−0.346345	−	0.126059i
$101$	3.67502	+	8.51965i	0.365678	+	0.847737i	0.997367	+	0.0725151i	$0.0231026\pi$
$101$	3.67502	+	8.51965i	0.365678	+	0.847737i	−0.631689	+	0.775222i	$0.717638\pi$
$102$		0			0
$103$	−4.20365	−	14.0412i	−0.414198	−	1.38352i	−0.869831	−	0.493349i	$-0.835772\pi$
$103$	−4.20365	−	14.0412i	−0.414198	−	1.38352i	0.455634	−	0.890167i	$-0.349413\pi$
$104$	16.9524	−	1.98145i	1.66232	−	0.194297i
$105$		0			0
$106$	0.191128	+	3.28154i	0.0185640	+	0.318731i
$107$	−0.0376376	−	0.0651902i	−0.00363856	−	0.00630218i	0.864200	−	0.503148i	$-0.167825\pi$
$107$	−0.0376376	−	0.0651902i	−0.00363856	−	0.00630218i	−0.867839	+	0.496846i	$0.834492\pi$
$108$		0			0
$109$	−2.64599	+	4.58298i	−0.253440	+	0.438970i	−0.964470	−	0.264191i	$-0.914895\pi$
$109$	−2.64599	+	4.58298i	−0.253440	+	0.438970i	0.711031	+	0.703161i	$0.248229\pi$
$110$	−1.47216	−	0.739347i	−0.140365	−	0.0704939i
$111$		0			0
$112$	0.261622	+	0.351419i	0.0247210	+	0.0332060i
$113$	18.0181	+	4.27037i	1.69500	+	0.401722i	0.960807	−	0.277219i	$-0.0894128\pi$
$113$	18.0181	+	4.27037i	1.69500	+	0.401722i	0.734193	+	0.678941i	$0.237561\pi$
$114$		0			0
$115$	0.690923	−	0.928071i	0.0644289	−	0.0865430i
$116$	3.95814	−	3.32128i	0.367504	−	0.308373i
$117$		0			0
$118$	1.03036	+	0.864571i	0.0948520	+	0.0795903i
$119$	−1.31370	+	0.311354i	−0.120427	+	0.0285417i
$120$		0			0
$121$	6.45430	+	4.24506i	0.586755	+	0.385915i
$122$	−2.46850	−	1.62356i	−0.223488	−	0.146990i
$123$		0			0
$124$	3.57441	−	0.847151i	0.320992	−	0.0760764i
$125$	−6.06315	−	5.08759i	−0.542305	−	0.455048i
$126$		0			0
$127$	8.52895	−	7.15664i	0.756822	−	0.635049i	−0.180476	−	0.983579i	$-0.557764\pi$
$127$	8.52895	−	7.15664i	0.756822	−	0.635049i	0.937297	+	0.348531i	$0.113319\pi$
$128$	−0.357982	+	0.480853i	−0.0316414	+	0.0425018i
$129$		0			0
$130$	4.95232	+	1.17372i	0.434347	+	0.102942i
$131$	−0.164790	−	0.221351i	−0.0143977	−	0.0193395i	0.794866	−	0.606785i	$-0.207541\pi$
$131$	−0.164790	−	0.221351i	−0.0143977	−	0.0193395i	−0.809264	+	0.587445i	$0.800134\pi$
$132$		0			0
$133$	−0.477868	−	0.239994i	−0.0414364	−	0.0208101i
$134$	3.34872	−	5.80016i	0.289285	−	0.501057i
$135$		0			0
$136$	7.19452	+	12.4613i	0.616925	+	1.06855i
$137$	0.612702	+	10.5197i	0.0523466	+	0.898757i	0.917621	+	0.397458i	$0.130107\pi$
$137$	0.612702	+	10.5197i	0.0523466	+	0.898757i	−0.865274	+	0.501299i	$0.832856\pi$
$138$		0			0
$139$	−0.538250	+	0.0629124i	−0.0456537	+	0.00533616i	−0.138889	−	0.990308i	$-0.544353\pi$
$139$	−0.538250	+	0.0629124i	−0.0456537	+	0.00533616i	0.0932354	+	0.995644i	$0.470279\pi$
$140$	−0.0605210	−	0.202154i	−0.00511496	−	0.0170851i
$141$		0			0
$142$	−5.44938	−	12.6331i	−0.457302	−	1.06014i
$143$	9.50717	+	3.46033i	0.795029	+	0.289367i
$144$		0			0
$145$	4.80349	−	1.74833i	0.398908	−	0.145191i
$146$	4.69903	+	4.98068i	0.388895	+	0.412204i
$147$		0			0
$148$	5.49741	−	2.76090i	0.451884	−	0.226945i
$149$	−1.14216	+	19.6101i	−0.0935693	+	1.60652i	0.545997	+	0.837787i	$0.316151\pi$
$149$	−1.14216	+	19.6101i	−0.0935693	+	1.60652i	−0.639566	+	0.768736i	$0.720886\pi$
$150$		0			0
$151$	−4.25389	+	14.2090i	−0.346177	+	1.15631i	0.590770	+	0.806840i	$0.298824\pi$
$151$	−4.25389	+	14.2090i	−0.346177	+	1.15631i	−0.936947	+	0.349471i	$0.886361\pi$
$152$	−0.989660	+	5.61264i	−0.0802720	+	0.455245i
$153$		0			0
$154$	0.0959829	+	0.544346i	0.00773452	+	0.0438647i
$155$	3.60960	+	0.421902i	0.289930	+	0.0338880i
$156$		0			0
$157$	−4.00801	+	4.24824i	−0.319874	+	0.339047i	−0.867280	−	0.497820i	$-0.834134\pi$
$157$	−4.00801	+	4.24824i	−0.319874	+	0.339047i	0.547406	+	0.836867i	$0.315615\pi$
$158$	3.00941	−	6.97659i	0.239415	−	0.555027i
$159$		0			0
$160$	−3.19166	+	2.09919i	−0.252323	+	0.165955i
$161$	−0.388211			−0.0305953
$162$		0			0
$163$	−6.88988			−0.539657			−0.269828	−	0.962908i	$-0.586967\pi$
$163$	−6.88988			−0.539657			−0.269828	+	0.962908i	$0.586967\pi$
$164$	8.27419	−	5.44202i	0.646106	−	0.424951i
$165$		0			0
$166$	5.72551	−	13.2732i	0.444385	−	1.03020i
$167$	−12.1766	+	12.9064i	−0.942252	+	0.998728i	0.0577483	+	0.998331i	$0.481608\pi$
$167$	−12.1766	+	12.9064i	−0.942252	+	0.998728i	−1.00000		0.000397221i	$0.999874\pi$
$168$		0			0
$169$	−18.1334	−	2.11949i	−1.39488	−	0.163038i
$170$	0.745077	+	4.22554i	0.0571448	+	0.324084i
$171$		0			0
$172$	−1.90597	+	10.8093i	−0.145329	+	0.824202i
$173$	4.01157	−	13.3996i	0.304994	−	1.01875i	−0.658848	−	0.752276i	$-0.728956\pi$
$173$	4.01157	−	13.3996i	0.304994	−	1.01875i	0.963842	−	0.266474i	$-0.0858588\pi$
$174$		0			0
$175$	−0.0711371	+	1.22138i	−0.00537746	+	0.0923274i
$176$	2.47343	−	1.24220i	0.186442	−	0.0936345i
$177$		0			0
$178$	−0.316229	−	0.335183i	−0.0237024	−	0.0251230i
$179$	−9.85261	+	3.58606i	−0.736418	+	0.268034i	−0.682879	−	0.730531i	$-0.739272\pi$
$179$	−9.85261	+	3.58606i	−0.736418	+	0.268034i	−0.0535392	+	0.998566i	$0.517050\pi$
$180$		0			0
$181$	11.6610	+	4.24426i	0.866755	+	0.315473i	0.736852	−	0.676054i	$-0.236311\pi$
$181$	11.6610	+	4.24426i	0.866755	+	0.315473i	0.129903	+	0.991527i	$0.458533\pi$
$182$	−0.676372	−	1.56801i	−0.0501361	−	0.116228i
$183$		0			0
$184$	1.18664	+	3.96365i	0.0874803	+	0.292204i
$185$	6.04487	−	0.706543i	0.444427	−	0.0519461i
$186$		0			0
$187$	0.495943	+	8.51501i	0.0362669	+	0.622679i
$188$	0.884358	+	1.53175i	0.0644984	+	0.111715i
$189$		0			0
$190$	−0.849737	+	1.47179i	−0.0616464	+	0.106775i
$191$	12.6284	+	6.34222i	0.913759	+	0.458907i	0.842589	−	0.538557i	$-0.181030\pi$
$191$	12.6284	+	6.34222i	0.913759	+	0.458907i	0.0711702	+	0.997464i	$0.477327\pi$
$192$		0			0
$193$	13.1675	+	17.6871i	0.947820	+	1.27314i	0.961945	+	0.273243i	$0.0880965\pi$
$193$	13.1675	+	17.6871i	0.947820	+	1.27314i	−0.0141245	+	0.999900i	$0.504496\pi$
$194$	10.4705	+	2.48154i	0.751735	+	0.178164i
$195$		0			0
$196$	3.56486	−	4.78844i	0.254633	−	0.342031i
$197$	1.28639	−	1.07941i	0.0916516	−	0.0769049i	−0.595811	−	0.803125i	$-0.703169\pi$
$197$	1.28639	−	1.07941i	0.0916516	−	0.0769049i	0.687462	+	0.726220i	$0.258725\pi$
$198$		0			0
$199$	8.18059	+	6.86433i	0.579906	+	0.486599i	0.884916	−	0.465750i	$-0.154215\pi$
$199$	8.18059	+	6.86433i	0.579906	+	0.486599i	−0.305010	+	0.952349i	$0.598660\pi$
$200$	12.6878	−	3.00706i	0.897161	−	0.212631i
$201$		0			0
$202$	−8.26629	−	5.43682i	−0.581614	−	0.382534i
$203$	−1.43298	−	0.942484i	−0.100575	−	0.0661494i
$204$		0			0
$205$	9.53350	−	2.25948i	0.665849	−	0.157809i
$206$	11.9726	+	10.0462i	0.834173	+	0.699954i
$207$		0			0
$208$	−6.55049	+	5.49652i	−0.454195	+	0.381115i
$209$	−2.01741	+	2.70985i	−0.139547	+	0.187444i
$210$		0			0
$211$	−10.1652	−	2.40919i	−0.699798	−	0.165855i	−0.134709	−	0.990885i	$-0.543010\pi$
$211$	−10.1652	−	2.40919i	−0.699798	−	0.165855i	−0.565089	+	0.825030i	$0.691158\pi$
$212$	1.58849	+	2.13371i	0.109098	+	0.146544i
$213$		0			0
$214$	0.0717306	+	0.0360245i	0.00490341	+	0.00246258i
$215$	−5.42938	+	9.40396i	−0.370281	+	0.641345i
$216$		0			0
$217$	−0.609682	−	1.05600i	−0.0413879	−	0.0716860i
$218$	−0.328112	−	5.63347i	−0.0222226	−	0.381547i
$219$		0			0
$220$	−1.32413	+	0.154769i	−0.0892730	+	0.0104345i
$221$	−7.55761	−	25.2442i	−0.508380	−	1.69811i
$222$		0			0
$223$	5.39966	+	12.5178i	0.361588	+	0.838256i	0.997772	+	0.0667182i	$0.0212528\pi$
$223$	5.39966	+	12.5178i	0.361588	+	0.838256i	−0.636184	+	0.771538i	$0.719488\pi$
$224$	1.20445	+	0.438385i	0.0804759	+	0.0292908i
$225$		0			0
$226$	−18.5548	+	6.75338i	−1.23424	+	0.449228i
$227$	−8.98971	−	9.52854i	−0.596668	−	0.632431i	0.356708	−	0.934216i	$-0.383899\pi$
$227$	−8.98971	−	9.52854i	−0.596668	−	0.632431i	−0.953376	+	0.301785i	$0.902418\pi$
$228$		0			0
$229$	1.54142	−	0.774128i	0.101860	−	0.0511559i	−0.397140	−	0.917758i	$-0.629997\pi$
$229$	1.54142	−	0.774128i	0.101860	−	0.0511559i	0.499000	+	0.866602i	$0.333701\pi$
$230$	−0.0717373	+	1.23168i	−0.00473021	+	0.0812146i
$231$		0			0
$232$	−5.24264	+	17.5116i	−0.344196	+	1.14970i
$233$	4.21198	−	23.8873i	0.275936	−	1.56491i	−0.460036	−	0.887900i	$-0.652164\pi$
$233$	4.21198	−	23.8873i	0.275936	−	1.56491i	0.735972	−	0.677011i	$-0.236725\pi$
$234$		0			0
$235$	0.303852	+	1.72323i	0.0198211	+	0.112411i
$236$	1.08111	+	0.126363i	0.0703741	+	0.00822555i
$237$		0			0
$238$	0.987951	−	1.04717i	0.0640394	−	0.0678778i
$239$	−8.77100	+	20.3335i	−0.567349	+	1.31526i	0.357139	+	0.934051i	$0.383752\pi$
$239$	−8.77100	+	20.3335i	−0.567349	+	1.31526i	−0.924488	+	0.381211i	$0.875507\pi$
$240$		0			0
$241$	15.1000	−	9.93144i	0.972677	−	0.639740i	0.0395241	−	0.999219i	$-0.487416\pi$
$241$	15.1000	−	9.93144i	0.972677	−	0.639740i	0.933153	+	0.359479i	$0.117045\pi$
$242$	−8.23764			−0.529536
$243$		0			0
$244$	−2.39098			−0.153067
$245$	4.93432	−	3.24535i	0.315242	−	0.207338i
$246$		0			0
$247$	4.13396	−	9.58361i	0.263038	−	0.609790i
$248$	−8.91821	+	9.45275i	−0.566307	+	0.600250i
$249$		0			0
$250$	8.38285	+	0.979815i	0.530178	+	0.0619689i
$251$	1.74420	+	9.89185i	0.110093	+	0.624368i	0.989063	+	0.147492i	$0.0471200\pi$
$251$	1.74420	+	9.89185i	0.110093	+	0.624368i	−0.878970	+	0.476876i	$0.841769\pi$
$252$		0			0
$253$	−0.425886	+	2.41532i	−0.0267752	+	0.151850i
$254$	−3.40502	+	11.3735i	−0.213650	+	0.713640i
$255$		0			0
$256$	0.947781	−	16.2728i	0.0592363	−	1.01705i
$257$	8.19846	−	4.11742i	0.511406	−	0.256838i	−0.174331	−	0.984687i	$-0.555776\pi$
$257$	8.19846	−	4.11742i	0.511406	−	0.256838i	0.685737	+	0.727849i	$0.259480\pi$
$258$		0			0
$259$	−1.40132	−	1.48531i	−0.0870739	−	0.0922929i
$260$	3.87029	−	1.40867i	0.240025	−	0.0873620i
$261$		0			0
$262$	0.276516	+	0.100643i	0.0170832	+	0.00621777i
$263$	9.41306	+	21.8219i	0.580434	+	1.34560i	0.915087	+	0.403257i	$0.132122\pi$
$263$	9.41306	+	21.8219i	0.580434	+	1.34560i	−0.334653	+	0.942342i	$0.608619\pi$
$264$		0			0
$265$	0.754766	+	2.52109i	0.0463649	+	0.154870i
$266$	0.566364	−	0.0661985i	0.0347260	−	0.00405889i
$267$		0			0
$268$	−0.315139	−	5.41072i	−0.0192502	−	0.330513i
$269$	−3.35091	−	5.80395i	−0.204309	−	0.353873i	0.745604	−	0.666390i	$-0.232161\pi$
$269$	−3.35091	−	5.80395i	−0.204309	−	0.353873i	−0.949912	+	0.312517i	$0.898828\pi$
$270$		0			0
$271$	4.74494	−	8.21848i	0.288235	−	0.499237i	−0.685154	−	0.728398i	$-0.740265\pi$
$271$	4.74494	−	8.21848i	0.288235	−	0.499237i	0.973388	+	0.229161i	$0.0735984\pi$
$272$	−6.44220	−	3.23539i	−0.390616	−	0.196175i
$273$		0			0
$274$	−6.70998	−	9.01307i	−0.405365	−	0.544499i
$275$	7.52097	+	1.78250i	0.453532	+	0.107489i
$276$		0			0
$277$	−0.827868	+	1.11202i	−0.0497418	+	0.0668148i	−0.826298	−	0.563233i	$-0.809557\pi$
$277$	−0.827868	+	1.11202i	−0.0497418	+	0.0668148i	0.776556	+	0.630048i	$0.216965\pi$
$278$	0.442668	−	0.371442i	0.0265494	−	0.0222776i
$279$		0			0
$280$	0.571880	+	0.479864i	0.0341764	+	0.0286774i
$281$	−15.5815	+	3.69287i	−0.929512	+	0.220298i	−0.667366	−	0.744730i	$-0.732578\pi$
$281$	−15.5815	+	3.69287i	−0.929512	+	0.220298i	−0.262146	+	0.965028i	$0.584430\pi$
$282$		0			0
$283$	0.262449	+	0.172616i	0.0156010	+	0.0102609i	0.557286	−	0.830321i	$-0.311843\pi$
$283$	0.262449	+	0.172616i	0.0156010	+	0.0102609i	−0.541685	+	0.840582i	$0.682213\pi$
$284$	−9.30221	−	6.11816i	−0.551985	−	0.363046i
$285$		0			0
$286$	−10.4976	+	2.48799i	−0.620739	+	0.147118i
$287$	−2.51826	−	2.11307i	−0.148648	−	0.124731i
$288$		0			0
$289$	3.99528	−	3.35244i	0.235016	−	0.197202i
$290$	−3.25503	+	4.37226i	−0.191142	+	0.256748i
$291$		0			0
$292$	5.39195	+	1.27792i	0.315540	+	0.0747844i
$293$	−11.1446	−	14.9698i	−0.651076	−	0.874547i	0.346915	−	0.937897i	$-0.387229\pi$
$293$	−11.1446	−	14.9698i	−0.651076	−	0.874547i	−0.997991	+	0.0633491i	$0.979822\pi$
$294$		0			0
$295$	0.962295	+	0.483283i	0.0560270	+	0.0281378i
$296$	−10.8817	+	18.8477i	−0.632488	+	1.09550i
$297$		0			0
$298$	−10.4732	−	18.1401i	−0.606696	−	1.05083i
$299$	−0.440569	−	7.56428i	−0.0254788	−	0.437454i
$300$		0			0
$301$	3.61877	−	0.422974i	0.208583	−	0.0243798i
$302$	−4.53607	−	15.1515i	−0.261022	−	0.871873i
$303$		0			0
$304$	−1.13095	−	2.62183i	−0.0648642	−	0.150372i
$305$	−2.22277	−	0.809023i	−0.127276	−	0.0463245i
$306$		0			0
$307$	25.4414	−	9.25992i	1.45202	−	0.528491i	0.508864	−	0.860847i	$-0.330066\pi$
$307$	25.4414	−	9.25992i	1.45202	−	0.528491i	0.943154	+	0.332356i	$0.107843\pi$
$308$	0.306960	+	0.325359i	0.0174907	+	0.0185391i
$309$		0			0
$310$	−3.46305	+	1.73921i	−0.196688	+	0.0987804i
$311$	−0.719941	+	12.3609i	−0.0408241	+	0.700923i	0.914359	+	0.404906i	$0.132696\pi$
$311$	−0.719941	+	12.3609i	−0.0408241	+	0.700923i	−0.955183	+	0.296017i	$0.904341\pi$
$312$		0			0
$313$	6.15560	−	20.5611i	0.347935	−	1.16218i	−0.587660	−	0.809108i	$-0.699951\pi$
$313$	6.15560	−	20.5611i	0.347935	−	1.16218i	0.935595	−	0.353076i	$-0.114864\pi$
$314$	1.08147	−	6.13334i	0.0610311	−	0.346124i
$315$		0			0
$316$	−1.06770	−	6.05524i	−0.0600629	−	0.340634i
$317$	−23.4460	−	2.74044i	−1.31686	−	0.153919i	−0.571511	−	0.820595i	$-0.693642\pi$
$317$	−23.4460	−	2.74044i	−1.31686	−	0.153919i	−0.745348	+	0.666676i	$0.767717\pi$
$318$		0			0
$319$	−7.43587	+	7.88156i	−0.416329	+	0.441283i
$320$	2.64780	−	6.13828i	0.148016	−	0.343140i
$321$		0			0
$322$	0.345861	−	0.227476i	0.0192741	−	0.0126768i
$323$	8.79912			0.489596
$324$		0			0
$325$	−23.8792			−1.32458
$326$	6.13826	−	4.03720i	0.339967	−	0.223600i
$327$		0			0
$328$	−13.8770	+	32.1706i	−0.766232	+	1.77633i
$329$	0.402900	−	0.427049i	0.0222126	−	0.0235439i
$330$		0			0
$331$	0.842076	+	0.0984246i	0.0462847	+	0.00540990i	0.139204	−	0.990264i	$-0.455546\pi$
$331$	0.842076	+	0.0984246i	0.0462847	+	0.00540990i	−0.0929190	+	0.995674i	$0.529620\pi$
$332$	−2.03134	−	11.5203i	−0.111484	−	0.632259i
$333$		0			0
$334$	3.28558	−	18.6334i	0.179779	−	1.01958i
$335$	1.53783	−	5.13672i	0.0840207	−	0.280649i
$336$		0			0
$337$	−0.118835	+	2.04032i	−0.00647336	+	0.111143i	−0.999997	−	0.00248306i	$-0.999210\pi$
$337$	−0.118835	+	2.04032i	−0.00647336	+	0.111143i	0.993524	+	0.113626i	$0.0362467\pi$
$338$	17.3971	−	8.73718i	0.946280	−	0.475240i
$339$		0			0
$340$	2.38281	+	2.52563i	0.129226	+	0.136972i
$341$	−7.23894	+	2.63476i	−0.392011	+	0.142680i
$342$		0			0
$343$	−3.74626	−	1.36353i	−0.202279	−	0.0736236i
$344$	−15.3801	−	35.6550i	−0.829237	−	1.92239i
$345$		0			0
$346$	4.27767	+	14.2884i	0.229969	+	0.768151i
$347$	−6.45936	+	0.754991i	−0.346757	+	0.0405300i	−0.287689	−	0.957724i	$-0.592887\pi$
$347$	−6.45936	+	0.754991i	−0.346757	+	0.0405300i	−0.0590678	+	0.998254i	$0.518813\pi$
$348$		0			0
$349$	−0.384965	−	6.60959i	−0.0206067	−	0.353803i	−0.992813	−	0.119677i	$-0.961814\pi$
$349$	−0.384965	−	6.60959i	−0.0206067	−	0.353803i	0.972206	−	0.234126i	$-0.0752229\pi$
$350$	−0.652302	−	1.12982i	−0.0348670	−	0.0603914i
$351$		0			0
$352$	4.04883	−	7.01279i	0.215804	−	0.373783i
$353$	0.270111	+	0.135655i	0.0143765	+	0.00722017i	0.455973	−	0.889994i	$-0.349291\pi$
$353$	0.270111	+	0.135655i	0.0143765	+	0.00722017i	−0.441596	+	0.897214i	$0.645588\pi$
$354$		0			0
$355$	−6.57763	−	8.83530i	−0.349105	−	0.468929i
$356$	−0.362860	−	0.0859995i	−0.0192316	−	0.00455796i
$357$		0			0
$358$	6.67650	−	8.96809i	0.352864	−	0.473978i
$359$	−3.14494	+	2.63892i	−0.165984	+	0.139277i	−0.721996	−	0.691897i	$-0.756775\pi$
$359$	−3.14494	+	2.63892i	−0.165984	+	0.139277i	0.556012	+	0.831174i	$0.312331\pi$
$360$		0			0
$361$	−11.8851	−	9.97274i	−0.625529	−	0.524881i
$362$	−12.8759	+	3.05164i	−0.676740	+	0.160390i
$363$		0			0
$364$	−1.15458	−	0.759381i	−0.0605166	−	0.0398024i
$365$	4.58023	+	3.01246i	0.239740	+	0.157680i
$366$		0			0
$367$	−8.75239	+	2.07435i	−0.456871	+	0.108280i	−0.452606	−	0.891711i	$-0.649506\pi$
$367$	−8.75239	+	2.07435i	−0.456871	+	0.108280i	−0.00426466	+	0.999991i	$0.501357\pi$
$368$	−1.58793	−	1.33243i	−0.0827767	−	0.0694579i
$369$		0			0
$370$	−4.97142	+	4.17152i	−0.258452	+	0.216867i
$371$	0.527285	−	0.708267i	0.0273753	−	0.0367714i
$372$		0			0
$373$	5.11858	+	1.21313i	0.265030	+	0.0628133i	0.360982	−	0.932573i	$-0.382441\pi$
$373$	5.11858	+	1.21313i	0.265030	+	0.0628133i	−0.0959522	+	0.995386i	$0.530590\pi$
$374$	−5.43130	−	7.29550i	−0.280846	−	0.377242i
$375$		0			0
$376$	−5.59173	−	2.80827i	−0.288371	−	0.144826i
$377$	16.7380	−	28.9911i	0.862053	−	1.49312i
$378$		0			0
$379$	−3.76722	−	6.52502i	−0.193509	−	0.335168i	0.752902	−	0.658133i	$-0.228654\pi$
$379$	−3.76722	−	6.52502i	−0.193509	−	0.335168i	−0.946411	+	0.322965i	$0.895320\pi$
$380$	0.0799664	+	1.37297i	0.00410219	+	0.0704319i
$381$		0			0
$382$	−14.9671	+	1.74940i	−0.765782	+	0.0895070i
$383$	−10.2165	−	34.1256i	−0.522040	−	1.74374i	−0.657996	−	0.753022i	$-0.728596\pi$
$383$	−10.2165	−	34.1256i	−0.522040	−	1.74374i	0.135955	−	0.990715i	$-0.456590\pi$
$384$		0			0
$385$	0.175276	+	0.406335i	0.00893288	+	0.0207088i
$386$	−22.0950	−	8.04193i	−1.12461	−	0.409324i
$387$		0			0
$388$	8.18276	−	2.97828i	0.415417	−	0.151199i
$389$	8.68991	+	9.21077i	0.440596	+	0.467005i	0.909173	−	0.416418i	$-0.136715\pi$
$389$	8.68991	+	9.21077i	0.440596	+	0.467005i	−0.468577	+	0.883423i	$0.655233\pi$
$390$		0			0
$391$	5.70844	−	2.86689i	0.288688	−	0.144985i
$392$	−1.22798	+	21.0837i	−0.0620226	+	1.06489i
$393$		0			0
$394$	−0.513567	+	1.71543i	−0.0258731	+	0.0864223i
$395$	1.05629	−	5.99053i	0.0531478	−	0.301416i
$396$		0			0
$397$	1.88601	+	10.6961i	0.0946564	+	0.536823i	0.994852	+	0.101337i	$0.0323122\pi$
$397$	1.88601	+	10.6961i	0.0946564	+	0.536823i	−0.900196	+	0.435486i	$0.856577\pi$
$398$	−11.3104	−	1.32200i	−0.566939	−	0.0662656i
$399$		0			0
$400$	−4.48304	+	4.75175i	−0.224152	+	0.237587i
$401$	−2.27311	+	5.26965i	−0.113514	+	0.263154i	−0.965497	−	0.260415i	$-0.916141\pi$
$401$	−2.27311	+	5.26965i	−0.113514	+	0.263154i	0.851983	+	0.523569i	$0.175400\pi$
$402$		0			0
$403$	19.8842	−	13.0781i	0.990505	−	0.651465i
$404$	−8.00667			−0.398347
$405$		0			0
$406$	1.82891			0.0907674
$407$	−10.7785	+	7.08910i	−0.534268	+	0.351394i
$408$		0			0
$409$	−11.7085	+	27.1434i	−0.578948	+	1.34215i	0.337245	+	0.941417i	$0.390505\pi$
$409$	−11.7085	+	27.1434i	−0.578948	+	1.34215i	−0.916193	+	0.400737i	$0.868754\pi$
$410$	−7.16952	+	7.59925i	−0.354078	+	0.375300i
$411$		0			0
$412$	12.5624	+	1.46833i	0.618903	+	0.0723394i
$413$	−0.0627404	−	0.355818i	−0.00308725	−	0.0175087i
$414$		0			0
$415$	2.00964	−	11.3972i	0.0986491	−	0.559467i
$416$	−7.17503	+	23.9663i	−0.351785	+	1.17504i
$417$		0			0
$418$	0.209464	−	3.59636i	0.0102452	−	0.175904i
$419$	7.98438	−	4.00990i	0.390062	−	0.195897i	−0.242949	−	0.970039i	$-0.578115\pi$
$419$	7.98438	−	4.00990i	0.390062	−	0.195897i	0.633012	+	0.774142i	$0.281819\pi$
$420$		0			0
$421$	−1.73759	−	1.84173i	−0.0846848	−	0.0897606i	0.683645	−	0.729814i	$-0.260394\pi$
$421$	−1.73759	−	1.84173i	−0.0846848	−	0.0897606i	−0.768330	+	0.640054i	$0.778912\pi$
$422$	10.4679	−	3.81001i	0.509570	−	0.185468i
$423$		0			0
$424$	−8.84319	−	3.21866i	−0.429463	−	0.156312i
$425$	−7.97367	−	18.4851i	−0.386780	−	0.896657i
$426$		0			0
$427$	0.227626	+	0.760322i	0.0110156	+	0.0367946i
$428$	0.0645180	−	0.00754107i	0.00311860	−	0.000364511i
$429$		0			0
$430$	−0.673263	−	11.5595i	−0.0324676	−	0.557448i
$431$	14.8594	+	25.7372i	0.715750	+	1.23972i	0.962669	+	0.270680i	$0.0872485\pi$
$431$	14.8594	+	25.7372i	0.715750	+	1.23972i	−0.246919	+	0.969036i	$0.579418\pi$
$432$		0			0
$433$	0.612994	−	1.06174i	0.0294586	−	0.0510238i	−0.850920	−	0.525295i	$-0.823955\pi$
$433$	0.612994	−	1.06174i	0.0294586	−	0.0510238i	0.880379	+	0.474271i	$0.157288\pi$
$434$	1.16195	+	0.583551i	0.0557752	+	0.0280114i
$435$		0			0
$436$	−2.72698	−	3.66298i	−0.130599	−	0.175425i
$437$	2.46193	+	0.583487i	0.117770	+	0.0279120i
$438$		0			0
$439$	−10.3661	+	13.9241i	−0.494748	+	0.664562i	−0.977436	−	0.211231i	$-0.932253\pi$
$439$	−10.3661	+	13.9241i	−0.494748	+	0.664562i	0.482689	+	0.875792i	$0.339660\pi$
$440$	3.61294	−	3.03162i	0.172240	−	0.144527i
$441$		0			0
$442$	21.5252	+	18.0618i	1.02385	+	0.859113i
$443$	11.6619	−	2.76392i	0.554073	−	0.131318i	0.0559651	−	0.998433i	$-0.482176\pi$
$443$	11.6619	−	2.76392i	0.554073	−	0.131318i	0.498108	+	0.867115i	$0.334028\pi$
$444$		0			0
$445$	−0.308234	−	0.202729i	−0.0146117	−	0.00961027i
$446$	−12.1456	−	7.98827i	−0.575109	−	0.378255i
$447$		0			0
$448$	−2.18254	+	0.517271i	−0.103115	+	0.0244388i
$449$	−15.0015	−	12.5878i	−0.707965	−	0.594053i	0.216063	−	0.976380i	$-0.430678\pi$
$449$	−15.0015	−	12.5878i	−0.707965	−	0.594053i	−0.924027	+	0.382327i	$0.875123\pi$
$450$		0			0
$451$	−15.9095	+	13.3497i	−0.749150	+	0.628611i
$452$	−9.54203	+	12.8172i	−0.448820	+	0.602869i
$453$		0			0
$454$	13.5924	+	3.22145i	0.637921	+	0.151190i
$455$	−0.816411	−	1.09663i	−0.0382739	−	0.0514108i
$456$		0			0
$457$	21.4625	+	10.7789i	1.00397	+	0.504215i	0.873286	−	0.487208i	$-0.161985\pi$
$457$	21.4625	+	10.7789i	1.00397	+	0.504215i	0.130689	+	0.991423i	$0.458281\pi$
$458$	−0.919654	+	1.59289i	−0.0429726	+	0.0744308i
$459$		0			0
$460$	0.499212	+	0.864661i	0.0232759	+	0.0403150i
$461$	−0.823736	−	14.1430i	−0.0383652	−	0.658705i	−0.961598	−	0.274463i	$-0.911500\pi$
$461$	−0.823736	−	14.1430i	−0.0383652	−	0.658705i	0.923232	−	0.384242i	$-0.125537\pi$
$462$		0			0
$463$	10.9340	−	1.27800i	0.508147	−	0.0593938i	0.141843	−	0.989889i	$-0.454697\pi$
$463$	10.9340	−	1.27800i	0.508147	−	0.0593938i	0.366304	+	0.930495i	$0.380623\pi$
$464$	−2.62660	−	8.77345i	−0.121937	−	0.407297i
$465$		0			0
$466$	10.2445	+	23.7495i	0.474569	+	1.10018i
$467$	−36.6170	−	13.3275i	−1.69443	−	0.616723i	−0.699261	−	0.714867i	$-0.746487\pi$
$467$	−36.6170	−	13.3275i	−1.69443	−	0.616723i	−0.995172	+	0.0981436i	$0.968710\pi$
$468$		0			0
$469$	−1.69059	+	0.615324i	−0.0780642	+	0.0284130i
$470$	−1.28045	−	1.35720i	−0.0590628	−	0.0626029i
$471$		0			0
$472$	−3.44115	+	1.72821i	−0.158392	+	0.0795472i
$473$	1.33837	−	22.9789i	0.0615381	−	1.05657i
$474$		0			0
$475$	2.28688	−	7.63872i	0.104929	−	0.350488i
$476$	0.202307	−	1.14734i	0.00927272	−	0.0525882i
$477$		0			0
$478$	−4.10044	−	23.2547i	−0.187550	−	1.06365i
$479$	14.0251	+	1.63930i	0.640825	+	0.0749017i	0.430299	−	0.902686i	$-0.358408\pi$
$479$	14.0251	+	1.63930i	0.640825	+	0.0749017i	0.210526	+	0.977588i	$0.432482\pi$
$480$		0			0
$481$	27.3510	−	28.9904i	1.24710	−	1.32185i
$482$	−7.63332	+	17.6960i	−0.347688	+	0.806032i
$483$		0			0
$484$	−5.56961	+	3.66319i	−0.253164	+	0.166509i
$485$	8.61486			0.391181
$486$		0			0
$487$	−11.6224			−0.526663			−0.263332	−	0.964705i	$-0.584821\pi$
$487$	−11.6224			−0.526663			−0.263332	+	0.964705i	$0.584821\pi$
$488$	7.06715	−	4.64814i	0.319915	−	0.210411i
$489$		0			0
$490$	−2.49438	+	5.78263i	−0.112685	+	0.261233i
$491$	−3.60508	+	3.82116i	−0.162695	+	0.172447i	−0.803593	−	0.595180i	$-0.797081\pi$
$491$	−3.60508	+	3.82116i	−0.162695	+	0.172447i	0.640898	+	0.767626i	$0.278562\pi$
$492$		0			0
$493$	28.0313	+	3.27639i	1.26247	+	0.147561i
$494$	1.93263	+	10.9605i	0.0869530	+	0.493135i
$495$		0			0
$496$	1.13061	−	6.41203i	0.0507660	−	0.287909i
$497$	−1.05997	+	3.54053i	−0.0475460	+	0.158815i
$498$		0			0
$499$	−0.320759	+	5.50722i	−0.0143592	+	0.246537i	0.983489	+	0.180968i	$0.0579232\pi$
$499$	−0.320759	+	5.50722i	−0.0143592	+	0.246537i	−0.997848	+	0.0655687i	$0.979114\pi$
$500$	6.10350	−	3.06529i	0.272957	−	0.137084i
$501$		0			0
$502$	−7.35016	−	7.79071i	−0.328054	−	0.347717i
$503$	31.2754	−	11.3833i	1.39450	−	0.507557i	0.467959	−	0.883750i	$-0.344989\pi$
$503$	31.2754	−	11.3833i	1.39450	−	0.507557i	0.926541	+	0.376193i	$0.122767\pi$
$504$		0			0
$505$	−7.44341	−	2.70918i	−0.331227	−	0.120557i
$506$	−1.03586	−	2.40139i	−0.0460495	−	0.106755i
$507$		0			0
$508$	2.75550	+	9.20402i	0.122256	+	0.408362i
$509$	−21.9142	+	2.56140i	−0.971328	+	0.113532i	−0.586932	−	0.809636i	$-0.699664\pi$
$509$	−21.9142	+	2.56140i	−0.971328	+	0.113532i	−0.384396	+	0.923168i	$0.625590\pi$
$510$		0			0
$511$	−0.106951	−	1.83628i	−0.00473124	−	0.0812323i
$512$	8.09134	+	14.0146i	0.357590	+	0.619364i
$513$		0			0
$514$	−4.89144	+	8.47222i	−0.215752	+	0.373694i
$515$	11.1818	+	5.61570i	0.492728	+	0.247457i
$516$		0			0
$517$	−2.21496	−	2.97520i	−0.0974137	−	0.130849i
$518$	2.11879	+	0.502162i	0.0930942	+	0.0220637i
$519$		0			0
$520$	−8.70114	+	11.6877i	−0.381570	+	0.512538i
$521$	−21.4866	+	18.0294i	−0.941345	+	0.789882i	−0.977819	−	0.209453i	$-0.932832\pi$
$521$	−21.4866	+	18.0294i	−0.941345	+	0.789882i	0.0364742	+	0.999335i	$0.488387\pi$
$522$		0			0
$523$	−6.29841	−	5.28500i	−0.275410	−	0.231097i	0.494612	−	0.869114i	$-0.335310\pi$
$523$	−6.29841	−	5.28500i	−0.275410	−	0.231097i	−0.770022	+	0.638017i	$0.779755\pi$
$524$	0.231712	−	0.0549167i	0.0101224	−	0.00239905i
$525$		0			0
$526$	−21.1730	−	13.9257i	−0.923186	−	0.607189i
$527$	16.7635	+	11.0255i	0.730229	+	0.480279i
$528$		0			0
$529$	−20.5927	+	4.88057i	−0.895337	+	0.212199i
$530$	−2.14969	−	1.80381i	−0.0933766	−	0.0783523i
$531$		0			0
$532$	0.353491	−	0.296614i	0.0153258	−	0.0128598i
$533$	38.3153	−	51.4664i	1.65962	−	2.22926i
$534$		0			0
$535$	0.0625308	+	0.0148201i	0.00270344	+	0.000640728i
$536$	11.4501	+	15.3802i	0.494569	+	0.664322i
$537$		0			0
$538$	6.38625	+	3.20729i	0.275331	+	0.138276i
$539$	−6.25951	+	10.8418i	−0.269616	+	0.466989i
$540$		0			0
$541$	0.833782	+	1.44415i	0.0358471	+	0.0620889i	0.883392	−	0.468634i	$-0.155254\pi$
$541$	0.833782	+	1.44415i	0.0358471	+	0.0620889i	−0.847545	+	0.530723i	$0.821920\pi$
$542$	0.588390	+	10.1023i	0.0252735	+	0.433930i
$543$		0			0
$544$	−20.9483	+	2.44850i	−0.898150	+	0.104979i
$545$	−1.29572	−	4.32801i	−0.0555025	−	0.185391i
$546$		0			0
$547$	7.06785	+	16.3851i	0.302199	+	0.700577i	0.999875	−	0.0158373i	$-0.00504139\pi$
$547$	7.06785	+	16.3851i	0.302199	+	0.700577i	−0.697675	+	0.716414i	$0.745782\pi$
$548$	−8.54475	−	3.11003i	−0.365013	−	0.132854i
$549$		0			0
$550$	−7.74498	+	2.81894i	−0.330247	+	0.120200i
$551$	7.67098	+	8.13076i	0.326795	+	0.346382i
$552$		0			0
$553$	−1.82390	+	0.915996i	−0.0775600	+	0.0389521i
$554$	0.0859560	−	1.47581i	0.00365192	−	0.0627010i
$555$		0			0
$556$	0.134119	−	0.447988i	0.00568790	−	0.0189989i
$557$	−3.03540	+	17.2146i	−0.128614	+	0.729407i	0.850481	+	0.526005i	$0.176311\pi$
$557$	−3.03540	+	17.2146i	−0.128614	+	0.729407i	−0.979095	+	0.203402i	$0.934800\pi$
$558$		0			0
$559$	12.3485	+	70.0317i	0.522285	+	2.96203i
$560$	−0.371490	−	0.0434210i	−0.0156983	−	0.00183487i
$561$		0			0
$562$	11.7178	−	12.4201i	0.494285	−	0.523912i
$563$	−13.6909	+	31.7390i	−0.577002	+	1.33764i	0.340626	+	0.940199i	$0.389361\pi$
$563$	−13.6909	+	31.7390i	−0.577002	+	1.33764i	−0.917628	+	0.397441i	$0.869898\pi$
$564$		0			0
$565$	−13.2076	+	8.68681i	−0.555650	+	0.365457i
$566$	−0.334965			−0.0140796
$567$		0			0
$568$	39.3890			1.65273
$569$	21.3130	−	14.0178i	0.893489	−	0.587657i	−0.0176099	−	0.999845i	$-0.505606\pi$
$569$	21.3130	−	14.0178i	0.893489	−	0.587657i	0.911099	+	0.412188i	$0.135235\pi$
$570$		0			0
$571$	8.79169	−	20.3814i	0.367921	−	0.852936i	−0.629210	−	0.777235i	$-0.716621\pi$
$571$	8.79169	−	20.3814i	0.367921	−	0.852936i	0.997131	−	0.0757007i	$-0.0241194\pi$
$572$	−5.99126	+	6.35036i	−0.250507	+	0.265522i
$573$		0			0
$574$	3.48172	+	0.406955i	0.145324	+	0.0169860i
$575$	−1.00519	−	5.70073i	−0.0419194	−	0.237737i
$576$		0			0
$577$	−3.76924	+	21.3764i	−0.156915	+	0.889911i	0.800098	+	0.599869i	$0.204781\pi$
$577$	−3.76924	+	21.3764i	−0.156915	+	0.889911i	−0.957014	+	0.290042i	$0.906331\pi$
$578$	−1.59504	+	5.32779i	−0.0663448	+	0.221607i
$579$		0			0
$580$	−0.256483	+	4.40364i	−0.0106499	+	0.182851i
$581$	−3.47003	+	1.74272i	−0.143961	+	0.0723000i
$582$		0			0
$583$	−3.82815	−	4.05760i	−0.158546	−	0.168049i
$584$	−18.4216	+	6.70492i	−0.762292	+	0.277452i
$585$		0			0
$586$	18.7006	+	6.80646i	0.772515	+	0.281172i
$587$	8.05782	+	18.6801i	0.332582	+	0.771012i	0.999661	+	0.0260249i	$0.00828492\pi$
$587$	8.05782	+	18.6801i	0.332582	+	0.771012i	−0.667079	+	0.744987i	$0.732456\pi$
$588$		0			0
$589$	2.27925	+	7.61323i	0.0939149	+	0.313698i
$590$	−1.14050	+	0.133306i	−0.0469538	+	0.00548811i
$591$		0			0
$592$	−0.633990	−	10.8852i	−0.0260568	−	0.447378i
$593$	−0.579087	−	1.00301i	−0.0237803	−	0.0411886i	0.853890	−	0.520453i	$-0.174237\pi$
$593$	−0.579087	−	1.00301i	−0.0237803	−	0.0411886i	−0.877671	+	0.479264i	$0.840904\pi$
$594$		0			0
$595$	0.576294	−	0.998171i	0.0236258	−	0.0409210i
$596$	−15.1478	−	7.60752i	−0.620479	−	0.311616i
$597$		0			0
$598$	4.82488	+	6.48094i	0.197304	+	0.265025i
$599$	44.1467	+	10.4629i	1.80378	+	0.427505i	0.988458	−	0.151498i	$-0.0484096\pi$
$599$	44.1467	+	10.4629i	1.80378	+	0.427505i	0.815326	+	0.579002i	$0.196558\pi$
$600$		0			0
$601$	−19.5190	+	26.2185i	−0.796195	+	1.06948i	0.199780	+	0.979841i	$0.435977\pi$
$601$	−19.5190	+	26.2185i	−0.796195	+	1.06948i	−0.995975	+	0.0896345i	$0.971430\pi$
$602$	−2.97615	+	2.49729i	−0.121299	+	0.101782i
$603$		0			0
$604$	−9.80464	−	8.22707i	−0.398945	−	0.334755i
$605$	−6.41729	+	1.52093i	−0.260900	+	0.0618344i
$606$		0			0
$607$	−0.512985	−	0.337395i	−0.0208214	−	0.0136945i	0.539056	−	0.842270i	$-0.318781\pi$
$607$	−0.512985	−	0.337395i	−0.0208214	−	0.0136945i	−0.559877	+	0.828576i	$0.689152\pi$
$608$	−6.97941	−	4.59043i	−0.283052	−	0.186167i
$609$		0			0
$610$	2.45435	−	0.581691i	0.0993736	−	0.0235520i
$611$	8.77827	+	7.36585i	0.355131	+	0.297990i
$612$		0			0
$613$	−15.6352	+	13.1195i	−0.631499	+	0.529891i	−0.901394	−	0.432999i	$-0.857455\pi$
$613$	−15.6352	+	13.1195i	−0.631499	+	0.529891i	0.269895	+	0.962890i	$0.413011\pi$
$614$	−17.2401	+	23.1574i	−0.695752	+	0.934557i
$615$		0			0
$616$	−1.53981	−	0.364942i	−0.0620407	−	0.0147039i
$617$	−5.77352	−	7.75518i	−0.232433	−	0.312212i	0.670570	−	0.741847i	$-0.266050\pi$
$617$	−5.77352	−	7.75518i	−0.232433	−	0.312212i	−0.903003	+	0.429635i	$0.858642\pi$
$618$		0			0
$619$	−24.0046	−	12.0556i	−0.964828	−	0.484555i	−0.104628	−	0.994511i	$-0.533365\pi$
$619$	−24.0046	−	12.0556i	−0.964828	−	0.484555i	−0.860200	+	0.509957i	$0.829661\pi$
$620$	−1.56802	+	2.71589i	−0.0629732	+	0.109073i
$621$		0			0
$622$	−6.60160	−	11.4343i	−0.264700	−	0.458474i
$623$	0.00719746	+	0.123576i	0.000288360	+	0.00495095i
$624$		0			0
$625$	−14.5002	+	1.69483i	−0.580008	+	0.0677932i
$626$	6.56393	+	21.9251i	0.262347	+	0.876302i
$627$		0			0
$628$	−1.99623	−	4.62778i	−0.0796581	−	0.184668i
$629$	31.5746	+	11.4922i	1.25896	+	0.458224i
$630$		0			0
$631$	29.6208	−	10.7811i	1.17918	−	0.429188i	0.323270	−	0.946307i	$-0.395218\pi$
$631$	29.6208	−	10.7811i	1.17918	−	0.429188i	0.855914	+	0.517119i	$0.172996\pi$
$632$	14.9275	+	15.8222i	0.593782	+	0.629372i
$633$		0			0
$634$	22.4941	−	11.2969i	0.893354	−	0.448659i
$635$	−0.552665	+	9.48889i	−0.0219318	+	0.376555i
$636$		0			0
$637$	11.0926	−	37.0519i	0.439505	−	1.46805i
$638$	2.00641	−	11.3789i	0.0794344	−	0.450495i
$639$		0			0
$640$	−0.0888692	−	0.504002i	−0.00351286	−	0.0199224i
$641$	−11.2656	−	1.31676i	−0.444965	−	0.0520089i	−0.109339	−	0.994004i	$-0.534874\pi$
$641$	−11.2656	−	1.31676i	−0.444965	−	0.0520089i	−0.335625	+	0.941996i	$0.608948\pi$
$642$		0			0
$643$	−9.07210	+	9.61586i	−0.357769	+	0.379213i	−0.881111	−	0.472910i	$-0.843204\pi$
$643$	−9.07210	+	9.61586i	−0.357769	+	0.379213i	0.523342	+	0.852123i	$0.324685\pi$
$644$	0.132686	−	0.307601i	0.00522857	−	0.0121212i
$645$		0			0
$646$	−7.83922	+	5.15594i	−0.308430	+	0.202858i
$647$	36.5943			1.43867			0.719336	−	0.694663i	$-0.244446\pi$
$647$	36.5943			1.43867			0.719336	+	0.694663i	$0.244446\pi$
$648$		0			0
$649$	−2.28261			−0.0896005
$650$	21.2743	−	13.9923i	0.834445	−	0.548823i
$651$		0			0
$652$	2.35488	−	5.45923i	0.0922244	−	0.213800i
$653$	18.7327	−	19.8555i	0.733069	−	0.777008i	−0.248394	−	0.968659i	$-0.579903\pi$
$653$	18.7327	−	19.8555i	0.733069	−	0.777008i	0.981463	+	0.191651i	$0.0613843\pi$
$654$		0			0
$655$	0.233993	+	0.0273499i	0.00914287	+	0.00106865i
$656$	−3.04809	−	17.2866i	−0.119008	−	0.674928i
$657$		0			0
$658$	−0.108714	+	0.616545i	−0.00423809	+	0.0240354i
$659$	−4.23303	+	14.1393i	−0.164895	+	0.550789i	0.835104	+	0.550091i	$0.185407\pi$
$659$	−4.23303	+	14.1393i	−0.164895	+	0.550789i	−1.00000		0.000697383i	$0.999778\pi$
$660$		0			0
$661$	1.61762	−	27.7734i	0.0629181	−	1.08026i	−0.808111	−	0.589030i	$-0.799510\pi$
$661$	1.61762	−	27.7734i	0.0629181	−	1.08026i	0.871029	−	0.491232i	$-0.163453\pi$
$662$	−0.807887	+	0.405736i	−0.0313994	+	0.0157694i
$663$		0			0
$664$	28.4000	+	30.1023i	1.10214	+	1.16820i
$665$	0.428987	−	0.156138i	0.0166354	−	0.00605479i
$666$		0			0
$667$	7.62568	+	2.77552i	0.295267	+	0.107469i
$668$	−6.06466	−	14.0595i	−0.234649	−	0.543977i
$669$		0			0
$670$	1.63984	+	5.47746i	0.0633527	+	0.211613i
$671$	4.98019	−	0.582101i	0.192258	−	0.0224718i
$672$		0			0
$673$	−1.91225	−	32.8321i	−0.0737118	−	1.26558i	−0.808992	−	0.587820i	$-0.799986\pi$
$673$	−1.91225	−	32.8321i	−0.0737118	−	1.26558i	0.735280	−	0.677763i	$-0.237051\pi$
$674$	−1.08967	−	1.88737i	−0.0419727	−	0.0726989i
$675$		0			0
$676$	7.87718	−	13.6437i	0.302968	−	0.524757i
$677$	21.5460	+	10.8208i	0.828081	+	0.415878i	0.811762	−	0.583989i	$-0.198509\pi$
$677$	21.5460	+	10.8208i	0.828081	+	0.415878i	0.0163192	+	0.999867i	$0.494805\pi$
$678$		0			0
$679$	−1.72610	−	2.31855i	−0.0662416	−	0.0889779i
$680$	−11.9529	−	2.83290i	−0.458374	−	0.108637i
$681$		0			0
$682$	4.90538	−	6.58907i	0.187837	−	0.252308i
$683$	10.1873	−	8.54816i	0.389806	−	0.327086i	−0.426731	−	0.904378i	$-0.640335\pi$
$683$	10.1873	−	8.54816i	0.389806	−	0.327086i	0.816538	+	0.577292i	$0.195891\pi$
$684$		0			0
$685$	−6.89130	−	5.78249i	−0.263303	−	0.220938i
$686$	4.13656	−	0.980382i	0.157934	−	0.0374311i
$687$		0			0
$688$	16.2539	+	10.6904i	0.619675	+	0.407567i
$689$	14.3990	+	9.47035i	0.548557	+	0.360792i
$690$		0			0
$691$	−42.6555	+	10.1095i	−1.62269	+	0.384585i	−0.938654	−	0.344862i	$-0.887926\pi$
$691$	−42.6555	+	10.1095i	−1.62269	+	0.384585i	−0.684038	+	0.729447i	$0.739778\pi$
$692$	9.24612	+	7.75841i	0.351485	+	0.294931i
$693$		0			0
$694$	5.31231	−	4.45756i	0.201653	−	0.169207i
$695$	0.276267	−	0.371091i	0.0104794	−	0.0140763i
$696$		0			0
$697$	52.6345	+	12.4746i	1.99367	+	0.472510i
$698$	4.21593	+	5.66297i	0.159575	+	0.214347i
$699$		0			0
$700$	−0.943452	−	0.473819i	−0.0356591	−	0.0179087i
$701$	3.65194	−	6.32534i	0.137932	−	0.238905i	−0.788782	−	0.614673i	$-0.789288\pi$
$701$	3.65194	−	6.32534i	0.137932	−	0.238905i	0.926714	+	0.375768i	$0.122621\pi$
$702$		0			0
$703$	6.65434	+	11.5257i	0.250973	+	0.434699i
$704$	0.823941	+	14.1465i	0.0310535	+	0.533167i
$705$		0			0
$706$	−0.320133	+	0.0374181i	−0.0120484	+	0.00140825i
$707$	0.762251	+	2.54609i	0.0286674	+	0.0957558i
$708$		0			0
$709$	−17.3188	−	40.1494i	−0.650420	−	1.50784i	−0.849350	−	0.527829i	$-0.823006\pi$
$709$	−17.3188	−	40.1494i	−0.650420	−	1.50784i	0.198931	−	0.980014i	$-0.436253\pi$
$710$	11.0372	+	4.01722i	0.414219	+	0.150764i
$711$		0			0
$712$	1.23971	−	0.451219i	0.0464602	−	0.0169101i
$713$	3.95917	+	4.19647i	0.148272	+	0.157159i
$714$		0			0
$715$	−7.71852	+	3.87638i	−0.288656	+	0.144969i
$716$	0.526080	−	9.03245i	0.0196605	−	0.337558i
$717$		0			0
$718$	1.25556	−	4.19385i	0.0468569	−	0.156513i
$719$	1.93615	−	10.9804i	0.0722061	−	0.409501i	−0.927185	−	0.374604i	$-0.877779\pi$
$719$	1.93615	−	10.9804i	0.0722061	−	0.409501i	0.999391	−	0.0348968i	$-0.0111103\pi$
$720$		0			0
$721$	−0.729037	−	4.13457i	−0.0271508	−	0.153980i
$722$	16.4321	+	1.92064i	0.611541	+	0.0714789i
$723$		0			0
$724$	−7.34856	+	7.78902i	−0.273107	+	0.289477i
$725$	10.1296	−	23.4831i	0.376204	−	0.872140i
$726$		0			0
$727$	−24.3067	+	15.9867i	−0.901484	+	0.592916i	−0.913422	−	0.407013i	$-0.866570\pi$
$727$	−24.3067	+	15.9867i	−0.901484	+	0.592916i	0.0119379	+	0.999929i	$0.496200\pi$
$728$	4.88893			0.181196
$729$		0			0
$730$	−5.84576			−0.216361
$731$	−50.0886	+	32.9438i	−1.85259	+	1.21847i
$732$		0			0
$733$	6.87604	−	15.9405i	0.253972	−	0.588774i	−0.742759	−	0.669559i	$-0.766483\pi$
$733$	6.87604	−	15.9405i	0.253972	−	0.588774i	0.996732	+	0.0807844i	$0.0257425\pi$
$734$	6.58210	−	6.97662i	0.242950	−	0.257512i
$735$		0			0
$736$	−6.02353	−	0.704050i	−0.222030	−	0.0259516i
$737$	1.97369	+	11.1933i	0.0727017	+	0.412312i
$738$		0			0
$739$	3.59215	−	20.3721i	0.132139	−	0.749400i	−0.844670	−	0.535288i	$-0.820203\pi$
$739$	3.59215	−	20.3721i	0.132139	−	0.749400i	0.976809	−	0.214112i	$-0.0686857\pi$
$740$	−1.50623	+	5.03117i	−0.0553703	+	0.184950i
$741$		0			0
$742$	−0.0547471	+	0.939971i	−0.00200983	+	0.0345074i
$743$	34.0508	−	17.1009i	1.24920	−	0.627373i	0.303632	−	0.952790i	$-0.401801\pi$
$743$	34.0508	−	17.1009i	1.24920	−	0.627373i	0.945571	+	0.325417i	$0.105505\pi$
$744$		0			0
$745$	−11.5081	−	12.1978i	−0.421623	−	0.446894i
$746$	−5.27104	+	1.91850i	−0.192986	+	0.0702413i
$747$		0			0
$748$	−6.91643	−	2.51737i	−0.252890	−	0.0920443i
$749$	−0.00854027	−	0.0197986i	−0.000312055	−	0.000723424i
$750$		0			0
$751$	−9.82318	−	32.8117i	−0.358453	−	1.19732i	−0.927125	−	0.374752i	$-0.877728\pi$
$751$	−9.82318	−	32.8117i	−0.358453	−	1.19732i	0.568672	−	0.822564i	$-0.307457\pi$
$752$	3.11375	−	0.363945i	0.113547	−	0.0132717i
$753$		0			0
$754$	2.07558	+	35.6363i	0.0755881	+	1.29780i
$755$	−6.33114	−	10.9659i	−0.230414	−	0.399088i
$756$		0			0
$757$	−14.5877	+	25.2666i	−0.530198	+	0.918330i	0.469181	+	0.883102i	$0.344549\pi$
$757$	−14.5877	+	25.2666i	−0.530198	+	0.918330i	−0.999379	+	0.0352284i	$0.988784\pi$
$758$	7.17966	+	3.60576i	0.260777	+	0.130967i
$759$		0			0
$760$	−2.90546	−	3.90271i	−0.105392	−	0.141566i
$761$	−12.0070	−	2.84572i	−0.435255	−	0.103157i	0.00714662	−	0.999974i	$-0.497725\pi$
$761$	−12.0070	−	2.84572i	−0.435255	−	0.103157i	−0.442401	+	0.896817i	$0.645873\pi$
$762$		0			0
$763$	−0.905200	+	1.21589i	−0.0327704	+	0.0440183i
$764$	−9.34155	+	7.83849i	−0.337965	+	0.283587i
$765$		0			0
$766$	29.0983	+	24.4163i	1.05136	+	0.882198i
$767$	6.86191	−	1.62630i	0.247769	−	0.0587224i
$768$		0			0
$769$	−2.31777	−	1.52442i	−0.0835810	−	0.0549721i	0.507031	−	0.861928i	$-0.330743\pi$
$769$	−2.31777	−	1.52442i	−0.0835810	−	0.0549721i	−0.590612	+	0.806956i	$0.701113\pi$
$770$	−0.394251	−	0.259303i	−0.0142078	−	0.00934464i
$771$		0			0
$772$	−18.5150	+	4.38813i	−0.666369	+	0.157932i
$773$	21.3606	+	17.9237i	0.768287	+	0.644669i	0.940270	−	0.340431i	$-0.110573\pi$
$773$	21.3606	+	17.9237i	0.768287	+	0.644669i	−0.171983	+	0.985100i	$0.555017\pi$
$774$		0			0
$775$	13.9283	−	11.6872i	0.500320	−	0.419818i
$776$	−18.3964	+	24.7107i	−0.660392	+	0.887061i
$777$		0			0
$778$	−13.1391	−	3.11402i	−0.471059	−	0.111643i
$779$	12.7941	+	17.1855i	0.458398	+	0.615735i
$780$		0			0
$781$	20.8652	+	10.4789i	0.746616	+	0.374964i
$782$	−3.40582	+	5.89906i	−0.121792	+	0.210950i
$783$		0			0
$784$	−5.29048	−	9.16338i	−0.188946	−	0.327263i
$785$	−0.289916	−	4.97767i	−0.0103476	−	0.177661i
$786$		0			0
$787$	1.39131	−	0.162621i	0.0495950	−	0.00579682i	−0.0912592	−	0.995827i	$-0.529089\pi$
$787$	1.39131	−	0.162621i	0.0495950	−	0.00579682i	0.140854	+	0.990030i	$0.455015\pi$
$788$	0.415603	+	1.38821i	0.0148052	+	0.0494530i
$789$		0			0
$790$	2.56915	+	5.95597i	0.0914064	+	0.211904i
$791$	4.98424	+	1.81411i	0.177219	+	0.0645025i
$792$		0			0
$793$	−14.5565	+	5.29815i	−0.516918	+	0.188143i
$794$	−7.94778	−	8.42415i	−0.282056	−	0.298962i
$795$		0			0
$796$	−8.23503	+	4.13579i	−0.291883	+	0.146589i
$797$	−0.651880	+	11.1924i	−0.0230908	+	0.396453i	0.966885	+	0.255214i	$0.0821459\pi$
$797$	−0.651880	+	11.1924i	−0.0230908	+	0.396453i	−0.989975	+	0.141240i	$0.954891\pi$
$798$		0			0
$799$	−2.77073	+	9.25489i	−0.0980214	+	0.327414i
$800$	−3.31883	+	18.8220i	−0.117338	+	0.665460i
$801$		0			0
$802$	−1.06268	−	6.02674i	−0.0375244	−	0.212812i
$803$	−11.5421	−	1.34908i	−0.407311	−	0.0476078i
$804$		0			0
$805$	0.227433	−	0.241065i	0.00801597	−	0.00849643i
$806$	−10.0518	+	23.3028i	−0.354061	+	0.820805i
$807$		0			0
$808$	23.6658	−	15.5652i	0.832560	−	0.547583i
$809$	−2.44943			−0.0861173			−0.0430587	−	0.999073i	$-0.513710\pi$
$809$	−2.44943			−0.0861173			−0.0430587	+	0.999073i	$0.513710\pi$
$810$		0			0
$811$	11.9053			0.418050			0.209025	−	0.977910i	$-0.432971\pi$
$811$	11.9053			0.418050			0.209025	+	0.977910i	$0.432971\pi$
$812$	1.23656	−	0.813297i	0.0433947	−	0.0285411i
$813$		0			0
$814$	5.44870	−	12.6315i	0.190977	−	0.442734i
$815$	4.03644	−	4.27837i	0.141390	−	0.149865i
$816$		0			0
$817$	−23.5850	−	2.75669i	−0.825135	−	0.0964444i
$818$	−5.47372	−	31.0430i	−0.191384	−	1.08539i
$819$		0			0
$820$	−1.46813	+	8.32619i	−0.0512694	+	0.290763i
$821$	6.96784	−	23.2742i	0.243179	−	0.812275i	−0.746049	−	0.665891i	$-0.768051\pi$
$821$	6.96784	−	23.2742i	0.243179	−	0.812275i	0.989228	−	0.146384i	$-0.0467634\pi$
$822$		0			0
$823$	−1.80431	+	30.9788i	−0.0628944	+	1.07985i	0.808254	+	0.588834i	$0.200413\pi$
$823$	−1.80431	+	30.9788i	−0.0628944	+	1.07985i	−0.871148	+	0.491020i	$0.836624\pi$
$824$	−39.9858	+	20.0816i	−1.39297	+	0.699576i
$825$		0			0
$826$	0.264392	+	0.280239i	0.00919936	+	0.00975075i
$827$	−9.52144	+	3.46552i	−0.331093	+	0.120508i	−0.502217	−	0.864741i	$-0.667482\pi$
$827$	−9.52144	+	3.46552i	−0.331093	+	0.120508i	0.171124	+	0.985249i	$0.445260\pi$
$828$		0			0
$829$	−16.7991	−	6.11438i	−0.583458	−	0.212361i	0.0333918	−	0.999442i	$-0.489369\pi$
$829$	−16.7991	−	6.11438i	−0.583458	−	0.212361i	−0.616850	+	0.787081i	$0.711591\pi$
$830$	4.88791	+	11.3315i	0.169662	+	0.393320i
$831$		0			0
$832$	−12.5559	−	41.9397i	−0.435298	−	1.45400i
$833$	32.3861	−	3.78539i	1.12211	−	0.131156i
$834$		0			0
$835$	−0.880782	−	15.1224i	−0.0304807	−	0.523334i
$836$	−1.45764	−	2.52470i	−0.0504135	−	0.0873187i
$837$		0			0
$838$	−4.76371	+	8.25099i	−0.164560	+	0.285026i
$839$	−22.0336	−	11.0657i	−0.760685	−	0.382030i	0.0257780	−	0.999668i	$-0.491794\pi$
$839$	−22.0336	−	11.0657i	−0.760685	−	0.382030i	−0.786463	+	0.617637i	$0.788090\pi$
$840$		0			0
$841$	4.09225	+	5.49684i	0.141112	+	0.189546i
$842$	2.62722	+	0.622662i	0.0905399	+	0.0214583i
$843$		0			0
$844$	5.38327	−	7.23098i	0.185300	−	0.248901i
$845$	11.9396	−	10.0185i	0.410734	−	0.344647i
$846$		0			0
$847$	1.69512	+	1.42237i	0.0582450	+	0.0488734i
$848$	4.58775	−	1.08732i	0.157544	−	0.0373386i
$849$		0			0
$850$	17.9353	+	11.7963i	0.615177	+	0.404608i
$851$	8.07225	+	5.30920i	0.276713	+	0.181997i
$852$		0			0
$853$	2.02471	−	0.479866i	0.0693249	−	0.0164303i	−0.195807	−	0.980642i	$-0.562733\pi$
$853$	2.02471	−	0.479866i	0.0693249	−	0.0164303i	0.265132	+	0.964212i	$0.414584\pi$
$854$	−0.648313	−	0.543999i	−0.0221848	−	0.0186153i
$855$		0			0
$856$	−0.176040	+	0.147715i	−0.00601691	+	0.00504879i
$857$	7.38060	−	9.91387i	0.252117	−	0.338651i	−0.657989	−	0.753027i	$-0.728593\pi$
$857$	7.38060	−	9.91387i	0.252117	−	0.338651i	0.910106	+	0.414376i	$0.136000\pi$
$858$		0			0
$859$	−38.1158	−	9.03362i	−1.30050	−	0.308223i	−0.478686	−	0.877986i	$-0.658887\pi$
$859$	−38.1158	−	9.03362i	−1.30050	−	0.308223i	−0.821809	+	0.569763i	$0.807035\pi$
$860$	−5.59558	−	7.51617i	−0.190808	−	0.256299i
$861$		0			0
$862$	−28.3193	−	14.2225i	−0.964560	−	0.484420i
$863$	−12.2220	+	21.1691i	−0.416040	+	0.720603i	−0.995537	−	0.0943715i	$-0.969916\pi$
$863$	−12.2220	+	21.1691i	−0.416040	+	0.720603i	0.579497	+	0.814975i	$0.303249\pi$
$864$		0			0
$865$	5.97048	+	10.3412i	0.203003	+	0.351611i
$866$	0.0760135	+	1.30510i	0.00258304	+	0.0443491i
$867$		0			0
$868$	1.04511	−	0.122156i	0.0354734	−	0.00414624i
$869$	3.69812	+	12.3526i	0.125450	+	0.419033i
$870$		0			0
$871$	−13.9082	−	32.2428i	−0.471261	−	1.09251i
$872$	15.1813	+	5.52553i	0.514102	+	0.187118i
$873$		0			0
$874$	−2.53525	+	0.922757i	−0.0857563	+	0.0312127i
$875$	−1.55582	−	1.64907i	−0.0525962	−	0.0557488i
$876$		0			0
$877$	−12.1192	+	6.08649i	−0.409236	+	0.205526i	−0.641494	−	0.767128i	$-0.721685\pi$
$877$	−12.1192	+	6.08649i	−0.409236	+	0.205526i	0.232258	+	0.972654i	$0.425389\pi$
$878$	1.07629	−	18.4793i	0.0363232	−	0.623645i
$879$		0			0
$880$	−0.677694	+	2.26366i	−0.0228451	+	0.0763079i
$881$	2.84380	−	16.1280i	0.0958101	−	0.543366i	−0.898686	−	0.438593i	$-0.855477\pi$
$881$	2.84380	−	16.1280i	0.0958101	−	0.543366i	0.994496	−	0.104774i	$-0.0334118\pi$
$882$		0			0
$883$	−7.98860	−	45.3056i	−0.268838	−	1.52465i	−0.757880	−	0.652394i	$-0.773765\pi$
$883$	−7.98860	−	45.3056i	−0.268838	−	1.52465i	0.489042	−	0.872260i	$-0.337347\pi$
$884$	22.5855	+	2.63986i	0.759631	+	0.0887882i
$885$		0			0
$886$	−8.77015	+	9.29581i	−0.294639	+	0.312299i
$887$	19.5768	−	45.3842i	0.657325	−	1.52385i	−0.183773	−	0.982969i	$-0.558831\pi$
$887$	19.5768	−	45.3842i	0.657325	−	1.52385i	0.841098	−	0.540882i	$-0.181910\pi$
$888$		0			0
$889$	2.66452	−	1.75248i	0.0893651	−	0.0587763i
$890$	0.393400			0.0131868
$891$		0			0
$892$	−11.7641			−0.393892
$893$	−3.19694	+	2.10266i	−0.106981	+	0.0703628i
$894$		0			0
$895$	3.54534	−	8.21901i	0.118508	−	0.274731i
$896$	−0.117838	+	0.124901i	−0.00393669	+	0.00417265i
$897$		0			0
$898$	20.7409	+	2.42427i	0.692133	+	0.0808988i
$899$	4.42618	+	25.1021i	0.147621	+	0.837201i
$900$		0			0
$901$	−2.52300	+	14.3086i	−0.0840532	+	0.476690i
$902$	6.35156	−	21.2157i	0.211484	−	0.706406i
$903$		0			0
$904$	3.28694	−	56.4345i	0.109322	−	1.87698i
$905$	−9.46713	+	4.75457i	−0.314698	+	0.158047i
$906$		0			0
$907$	32.8053	+	34.7716i	1.08928	+	1.15457i	0.987149	+	0.159802i	$0.0510856\pi$
$907$	32.8053	+	34.7716i	1.08928	+	1.15457i	0.102134	+	0.994771i	$0.467433\pi$
$908$	10.6226	−	3.86630i	0.352523	−	0.128308i
$909$		0			0
$910$	1.36993	+	0.498614i	0.0454127	+	0.0165289i
$911$	13.1560	+	30.4989i	0.435876	+	1.01047i	0.984656	+	0.174508i	$0.0558333\pi$
$911$	13.1560	+	30.4989i	0.435876	+	1.01047i	−0.548780	+	0.835967i	$0.684907\pi$
$912$		0			0
$913$	7.03582	+	23.5013i	0.232852	+	0.777778i
$914$	−25.4372	+	2.97318i	−0.841387	+	0.0983441i
$915$		0			0
$916$	0.0865461	+	1.48594i	0.00285956	+	0.0490968i
$917$	−0.0395228	−	0.0684554i	−0.00130516	−	0.00226060i
$918$		0			0
$919$	13.4983	−	23.3798i	0.445268	−	0.771228i	−0.552802	−	0.833312i	$-0.686442\pi$
$919$	13.4983	−	23.3798i	0.445268	−	0.771228i	0.998071	+	0.0620848i	$0.0197749\pi$
$920$	−3.15648	−	1.58525i	−0.104066	−	0.0522640i
$921$		0			0
$922$	9.02111	+	12.1175i	0.297094	+	0.399067i
$923$	−70.1901	−	16.6354i	−2.31034	−	0.547560i
$924$		0			0
$925$	18.1828	−	24.4238i	0.597848	−	0.803049i
$926$	−8.99236	+	7.54549i	−0.295507	+	0.247960i
$927$		0			0
$928$	−20.5250	−	17.2225i	−0.673766	−	0.565357i
$929$	−0.850096	+	0.201476i	−0.0278907	+	0.00661023i	−0.244538	−	0.969640i	$-0.578636\pi$
$929$	−0.850096	+	0.201476i	−0.0278907	+	0.00661023i	0.216647	+	0.976250i	$0.430488\pi$
$930$		0			0
$931$	10.7902	+	7.09682i	0.353634	+	0.232589i
$932$	17.4877	+	11.5018i	0.572828	+	0.376755i
$933$		0			0
$934$	40.4318	−	9.58252i	1.32297	−	0.313550i
$935$	−5.57807	−	4.68056i	−0.182422	−	0.153071i
$936$		0			0
$937$	12.6271	−	10.5954i	0.412511	−	0.346138i	−0.412795	−	0.910824i	$-0.635447\pi$
$937$	12.6271	−	10.5954i	0.412511	−	0.346138i	0.825306	+	0.564686i	$0.191003\pi$
$938$	1.14561	−	1.53882i	0.0374054	−	0.0502442i
$939$		0			0
$940$	−1.46927	−	0.348222i	−0.0479222	−	0.0113578i
$941$	−18.1527	−	24.3833i	−0.591760	−	0.794872i	0.400860	−	0.916140i	$-0.368712\pi$
$941$	−18.1527	−	24.3833i	−0.591760	−	0.794872i	−0.992620	+	0.121267i	$0.961304\pi$
$942$		0			0
$943$	13.8995	+	6.98060i	0.452631	+	0.227320i
$944$	0.964622	−	1.67077i	0.0313958	−	0.0543791i
$945$		0			0
$946$	12.2723	+	21.2563i	0.399008	+	0.691102i
$947$	−0.743799	−	12.7705i	−0.0241702	−	0.414987i	−0.988592	−	0.150618i	$-0.951874\pi$
$947$	−0.743799	−	12.7705i	−0.0241702	−	0.414987i	0.964422	−	0.264368i	$-0.0851635\pi$
$948$		0			0
$949$	35.6585	−	4.16789i	1.15753	−	0.135295i
$950$	2.43858	+	8.14543i	0.0791181	+	0.264273i
$951$		0			0
$952$	1.63249	+	3.78455i	0.0529095	+	0.122658i
$953$	28.8328	+	10.4943i	0.933986	+	0.339943i	0.763788	−	0.645467i	$-0.223337\pi$
$953$	28.8328	+	10.4943i	0.933986	+	0.339943i	0.170198	+	0.985410i	$0.445559\pi$
$954$		0			0
$955$	−11.3367	+	4.12620i	−0.366845	+	0.133521i
$956$	−13.1135	−	13.8995i	−0.424121	−	0.449542i
$957$		0			0
$958$	−13.4557	+	6.75771i	−0.434734	+	0.218332i
$959$	−0.175504	+	3.01328i	−0.00566731	+	0.0973039i
$960$		0			0
$961$	3.69361	−	12.3375i	0.119149	−	0.397985i
$962$	−7.38006	+	41.8544i	−0.237943	+	1.34944i
$963$		0			0
$964$	2.70821	+	15.3590i	0.0872257	+	0.494681i
$965$	−18.6973	−	2.18540i	−0.601886	−	0.0703504i
$966$		0			0
$967$	−11.6005	+	12.2958i	−0.373047	+	0.395407i	−0.886513	−	0.462703i	$-0.846880\pi$
$967$	−11.6005	+	12.2958i	−0.373047	+	0.395407i	0.513466	+	0.858110i	$0.328361\pi$
$968$	9.34106	−	21.6550i	0.300233	−	0.696019i
$969$		0			0
$970$	−7.67506	+	5.04797i	−0.246431	+	0.162081i
$971$	−53.7751			−1.72572			−0.862862	−	0.505439i	$-0.831330\pi$
$971$	−53.7751			−1.72572			−0.862862	+	0.505439i	$0.831330\pi$
$972$		0			0
$973$	−0.155227			−0.00497635
$974$	10.3545	−	6.81029i	0.331781	−	0.218216i
$975$		0			0
$976$	−1.67853	+	3.89128i	−0.0537286	+	0.124557i
$977$	−10.1987	+	10.8100i	−0.326285	+	0.345841i	−0.869663	−	0.493647i	$-0.835664\pi$
$977$	−10.1987	+	10.8100i	−0.326285	+	0.345841i	0.543378	+	0.839488i	$0.317145\pi$
$978$		0			0
$979$	0.776743	+	0.0907883i	0.0248248	+	0.00290161i
$980$	0.884978	+	5.01896i	0.0282696	+	0.160325i
$981$		0			0
$982$	0.972752	−	5.51675i	0.0310418	−	0.176047i
$983$	5.10312	−	17.0456i	0.162764	−	0.543671i	−0.837231	−	0.546850i	$-0.815827\pi$
$983$	5.10312	−	17.0456i	0.162764	−	0.543671i	0.999995	+	0.00317929i	$0.00101200\pi$
$984$		0			0
$985$	−0.0833566	+	1.43118i	−0.00265596	+	0.0456011i
$986$	−26.8932	+	13.5063i	−0.856454	+	0.430127i
$987$		0			0
$988$	6.18068	+	6.55114i	0.196634	+	0.208420i
$989$	−16.1990	+	5.89594i	−0.515097	+	0.187480i
$990$		0			0
$991$	12.0174	+	4.37398i	0.381746	+	0.138944i	0.525763	−	0.850631i	$-0.323780\pi$
$991$	12.0174	+	4.37398i	0.381746	+	0.138944i	−0.144017	+	0.989575i	$0.546002\pi$
$992$	−7.54477	−	17.4907i	−0.239547	−	0.555332i
$993$		0			0
$994$	−1.13028	−	3.77539i	−0.0358503	−	0.119748i
$995$	−9.05510	+	1.05839i	−0.287066	+	0.0335532i
$996$		0			0
$997$	3.57455	+	61.3726i	0.113207	+	1.94369i	0.284940	+	0.958545i	$0.408026\pi$
$997$	3.57455	+	61.3726i	0.113207	+	1.94369i	−0.171733	+	0.985144i	$0.554937\pi$
$998$	−2.94125	−	5.09439i	−0.0931036	−	0.161260i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	729.2.g.a.28.3		144
3.2	odd	2		729.2.g.d.28.6		144
9.2	odd	6		729.2.g.c.271.3		144
9.4	even	3		243.2.g.a.91.3		144
9.5	odd	6		81.2.g.a.40.6	✓	144
9.7	even	3		729.2.g.b.271.6		144
81.2	odd	54		729.2.g.c.460.3		144
81.25	even	27		243.2.g.a.235.3		144
81.29	odd	54		729.2.g.d.703.6		144
81.32	odd	54		6561.2.a.c.1.27		72
81.49	even	27		6561.2.a.d.1.46		72
81.52	even	27	inner	729.2.g.a.703.3		144
81.56	odd	54		81.2.g.a.79.6	yes	144
81.79	even	27		729.2.g.b.460.6		144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
81.2.g.a.40.6	✓	144	9.5	odd	6
81.2.g.a.79.6	yes	144	81.56	odd	54
243.2.g.a.91.3		144	9.4	even	3
243.2.g.a.235.3		144	81.25	even	27
729.2.g.a.28.3		144	1.1	even	1	trivial
729.2.g.a.703.3		144	81.52	even	27	inner
729.2.g.b.271.6		144	9.7	even	3
729.2.g.b.460.6		144	81.79	even	27
729.2.g.c.271.3		144	9.2	odd	6
729.2.g.c.460.3		144	81.2	odd	54
729.2.g.d.28.6		144	3.2	odd	2
729.2.g.d.703.6		144	81.29	odd	54
6561.2.a.c.1.27		72	81.32	odd	54
6561.2.a.d.1.46		72	81.49	even	27

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 729 = 3^{6} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	729.g (of order \(27\), degree \(18\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.890910 + 0.585961i) q^{2} +(-0.341789 + 0.792356i) q^{4} +(-0.585850 + 0.620965i) q^{5} +(0.284505 + 0.0332539i) q^{7} +(-0.530120 - 3.00646i) q^{8} +O(q^{10})\)	\(q+(-0.890910 + 0.585961i) q^{2} +(-0.341789 + 0.792356i) q^{4} +(-0.585850 + 0.620965i) q^{5} +(0.284505 + 0.0332539i) q^{7} +(-0.530120 - 3.00646i) q^{8} +(0.158079 - 0.896509i) q^{10} +(0.519011 - 1.73362i) q^{11} +(-0.325075 + 5.58132i) q^{13} +(-0.272954 + 0.137083i) q^{14} +(1.04960 + 1.11251i) q^{16} +(-4.42908 + 1.61205i) q^{17} +(-1.75427 - 0.638503i) q^{19} +(-0.291788 - 0.676441i) q^{20} +(0.553440 + 1.84862i) q^{22} +(-1.34612 + 0.157339i) q^{23} +(0.248347 + 4.26396i) q^{25} +(-2.98082 - 5.16294i) q^{26} +(-0.123590 + 0.214064i) q^{28} +(-5.35083 - 2.68729i) q^{29} +(-2.54206 - 3.41458i) q^{31} +(4.35412 + 1.03194i) q^{32} +(3.00131 - 4.03146i) q^{34} +(-0.187327 + 0.157186i) q^{35} +(-5.46107 - 4.58238i) q^{37} +(1.93704 - 0.459086i) q^{38} +(2.17748 + 1.43215i) q^{40} +(-9.58849 - 6.30645i) q^{41} +(12.3767 - 2.93332i) q^{43} +(1.19625 + 1.00377i) q^{44} +(1.10708 - 0.928949i) q^{46} +(1.22397 - 1.64408i) q^{47} +(-6.73148 - 1.59539i) q^{49} +(-2.71977 - 3.65328i) q^{50} +(-4.31129 - 2.16521i) q^{52} +(1.54131 - 2.66962i) q^{53} +(0.772454 + 1.33793i) q^{55} +(-0.0508455 - 0.872983i) q^{56} +(6.34175 - 0.741244i) q^{58} +(-0.361763 - 1.20837i) q^{59} +(1.09744 + 2.54416i) q^{61} +(4.26556 + 1.55254i) q^{62} +(-7.35831 + 2.67821i) q^{64} +(-3.27536 - 3.47168i) q^{65} +(-5.61273 + 2.81882i) q^{67} +(0.236491 - 4.06039i) q^{68} +(0.0747867 - 0.249805i) q^{70} +(-2.24048 + 12.7064i) q^{71} +(-1.11508 - 6.32396i) q^{73} +(7.55042 + 0.882517i) q^{74} +(1.10551 - 1.17178i) q^{76} +(0.205311 - 0.475965i) q^{77} +(-5.95312 + 3.91543i) q^{79} -1.30574 q^{80} +12.2378 q^{82} +(-11.3260 + 7.44925i) q^{83} +(1.59375 - 3.69472i) q^{85} +(-9.30768 + 9.86557i) q^{86} +(-5.48720 - 0.641362i) q^{88} +(0.0750415 + 0.425581i) q^{89} +(-0.278086 + 1.57711i) q^{91} +(0.335421 - 1.12038i) q^{92} +(-0.127083 + 2.18193i) q^{94} +(1.42423 - 0.715275i) q^{95} +(-6.92494 - 7.34001i) q^{97} +(6.93197 - 2.52303i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8}+O(q^{10}) \) 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8	\( 144 q - 9 q^{2} + 9 q^{4} - 9 q^{5} + 9 q^{7} + 18 q^{8} - 18 q^{10} - 9 q^{11} + 9 q^{13} - 9 q^{14} + 9 q^{16} + 18 q^{17} - 18 q^{19} - 45 q^{20} + 9 q^{22} + 45 q^{23} + 9 q^{25} - 45 q^{26} - 9 q^{28} - 36 q^{29} + 9 q^{31} + 99 q^{32} + 9 q^{34} - 9 q^{35} - 18 q^{37} - 18 q^{38} + 9 q^{40} - 27 q^{41} + 9 q^{43} - 54 q^{44} - 18 q^{46} + 99 q^{47} + 9 q^{49} - 126 q^{50} - 27 q^{52} - 45 q^{53} - 9 q^{55} + 225 q^{56} + 9 q^{58} - 72 q^{59} + 9 q^{61} - 81 q^{62} - 18 q^{64} + 81 q^{65} - 45 q^{67} - 117 q^{68} - 99 q^{70} + 90 q^{71} - 18 q^{73} - 81 q^{74} - 153 q^{76} - 81 q^{77} - 99 q^{79} + 288 q^{80} - 36 q^{82} - 45 q^{83} - 99 q^{85} - 81 q^{86} - 153 q^{88} + 81 q^{89} - 18 q^{91} - 207 q^{92} - 99 q^{94} + 171 q^{95} - 45 q^{97} - 81 q^{98}+O(q^{100}) \) 144 * q - 9 * q^2 + 9 * q^4 - 9 * q^5 + 9 * q^7 + 18 * q^8 - 18 * q^10 - 9 * q^11 + 9 * q^13 - 9 * q^14 + 9 * q^16 + 18 * q^17 - 18 * q^19 - 45 * q^20 + 9 * q^22 + 45 * q^23 + 9 * q^25 - 45 * q^26 - 9 * q^28 - 36 * q^29 + 9 * q^31 + 99 * q^32 + 9 * q^34 - 9 * q^35 - 18 * q^37 - 18 * q^38 + 9 * q^40 - 27 * q^41 + 9 * q^43 - 54 * q^44 - 18 * q^46 + 99 * q^47 + 9 * q^49 - 126 * q^50 - 27 * q^52 - 45 * q^53 - 9 * q^55 + 225 * q^56 + 9 * q^58 - 72 * q^59 + 9 * q^61 - 81 * q^62 - 18 * q^64 + 81 * q^65 - 45 * q^67 - 117 * q^68 - 99 * q^70 + 90 * q^71 - 18 * q^73 - 81 * q^74 - 153 * q^76 - 81 * q^77 - 99 * q^79 + 288 * q^80 - 36 * q^82 - 45 * q^83 - 99 * q^85 - 81 * q^86 - 153 * q^88 + 81 * q^89 - 18 * q^91 - 207 * q^92 - 99 * q^94 + 171 * q^95 - 45 * q^97 - 81 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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